Graph the function and analyze it for domain, range, continuity, increasing or decreaseing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior.
f(x) = 3 * 0.2^x
Answers
Answer:
[tex]f(x) = 3 \cdot 0.2^x[/tex]
Step-by-step explanation:
[tex]f(x) = 3 \cdot 0.2^x[/tex]
Domain of f: "What values of x can we plug into this equation?" This makes sense for all real numbers so the domain is [tex]\mathbb{R}[/tex]
Range of f: "What values of f(x) can we get out of the function?" From the graph we see we can get any real number greater than 0 out of the function by choosing a suitable x-value in the domain. The range is therefore [tex](0, \infty)[/tex].
Continuity: Since the graph is one, unbroken curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We see that "roughly speaking" the function is continuous.
Increasing or decreasing behaviour: For all x in the domain, as x increases, f(x) decreases. This means the function exhibits decreasing behaviour.
Symmetry: It is clear to see the graph of f(x) has no symmetry.
Boundedness: Looking at the graph we see it is unbounded above as when we choose negative values, the graph of f(x) explodes upwards exponentially. Choose a value of x, plug it in, next choose (x-1), plug this in and we observe [tex]f(x-1) > f(x)[/tex] for all x in the domain.
The function is however bounded below by 0: no value of x in the domain exists which satisfies [tex]f(x) < 0[/tex].
Extrema: As far as I can tell, there are no turning points on the curve. (Is this what you mean by extrema?)
Asymptotes: Contrary to the curve's appearance, there are no vertical asymtotes for this curve. The negative-x portion of the curve is just growing so quickly it appears to look like an asymptote. There is a value of f(x) for all x<0. There is however a horizontal asymtote: [tex]y=0[/tex].
End behaviour: As [tex]x \rightarrow \infty, f(x) \rightarrow 0[/tex]. As [tex]x \rightarrow -\infty, f(x) \rightarrow +\infty[/tex]
The function f(x) = 3*0.2^x is a decaying exponential function, with a domain of all real numbers and a range of (0, ∞). It is continuous, decreasing and has a horizontal asymptote at y=0.
Explanation:The function f(x) = 3*0.2^x is an exponential function with a base of 0.2. Here we're multiplying the function by a coefficient of 3.
Domain: The domain of an exponential function is always all real numbers. So, the domain is (-∞, ∞).
Range: Since this is a decaying exponential function, the output will always be between 0 (which will never actually be reached) and positive infinity. So, the range is (0, ∞).
Continuity: An exponential function is always continuous, meaning there are no holes or jumps in the graph.
Increasing or Decreasing Behavior: Since the base of the exponential (0.2) is less than 1, this function is always decreasing.
Symmetry: Exponential functions are not symmetric.
Boundedness: This function is bounded below by 0.
Extrema: There are no maximum or minimum points in this function. However, it is worth noting that the function gets closer and closer to y=0 as x goes to infinity, but never reaches it. This is sometimes considered a minimum.
Asymptotes: An asymptote is a line that the graph approaches but never reaches. For this function, the x-axis, or y = 0, is the horizontal asymptote.
End behavior: As x approaches positive infinity, y approaches 0; as x approaches negative infinity, y approaches positive infinity.
Learn more about Function Analysis here:https://brainly.com/question/34156091
#SPJ11
Related Questions
Simplify 8^10 ÷ 8^5.
8^15
8^5
8^2
8^50
Answers
Answer:
8^5
Step-by-step explanation:
When we divide exponents with the same base, we subtract the exponents
8^10 ÷ 8^5
8^ (10-5)
8^5
Answer:
8^5 Disclaimer this is not the complete simplification. (see below)
Step-by-step explanation:
Simplify the following:
8^10/8^5
Hint: | For all exponents, a^n/a^m = a^(n - m). Apply this to 8^10/8^5.
Combine powers. 8^10/8^5 = 8^(10 - 5):
8^(10 - 5)
Hint: | Subtract 5 from 10.
10 - 5 = 5:
8^5
Hint: | Compute 8^5 by repeated squaring. For example a^7 = a a^6 = a (a^3)^2 = a (a a^2)^2.
8^5 = 8×8^4 = 8 (8^2)^2:
8 (8^2)^2
Hint: | Evaluate 8^2.
8^2 = 64:
8×64^2
Hint: | Evaluate 64^2.
| | 6 | 4
× | | 6 | 4
| 2 | 5 | 6
3 | 8 | 4 | 0
4 | 0 | 9 | 6:
8×4096
Can someone pls help me solve this question!!!!!!!
Answers
Total of 90 fish:
c + p = 90
Charlie gave 1/4 c to Peter. Now
Charlie has c - (1/4) c
Peter has p + (1/4) c
Peter gave 2/5 of his to Charlie. Now
Peter has p + (1/4) c - 2/5( p + (1/4) c )
Charlie has c - (1/4) c + 2/5( p + (1/4) c )
And then they had equal number:
c - (1/4) c + 2/5( p + (1/4) c ) = p + (1/4) c - 2/5( p + (1/4) c )
Let's do the easy subtractions then multiply by 20 to clear the fractions,
(3/4) c + 2/5( p + (1/4) c ) = 3/5( p + (1/4) c )
15c + 8p + 2c = 12p + 3c
14c = 4p
7c = 2p
c + p = 90
2c + 2p = 180
2c + 7c = 180
9c = 180
c = 20
p = 70
Answer: Charlie started with 20, Peter with 70
Check:
Initially C:20, P:70
1/4(20)=5 to P
C:15, P:75
(2/5) 75 = 30 to C
C:45, P45
Good
sin ( pi/4 - B) =
Please explain!
Answers
Answer:
sqrt2/2 ( cos b - sin b)
Step-by-step explanation:
I know thats the answer but I have no idea how you solve to get it. Im looking for help too.
Describe how you can use compatible numbers to estimate 17 x 27
Answers
Answer:
600
Step-by-step explanation:
Well, the closest number for 17 is 20, and for 27 is 30.
When we multiply those two numbers :
20*30=600
We got 600
To estimate 17 x 27 using compatible numbers, round 17 to 20 and 27 to 25, then multiply to get an estimated product of 500.
Using compatible numbers to estimate the product of 17 x 27 involves finding numbers close to 17 and 27 that are easier to multiply mentally, such as multiples of 10.
A good choice here would be to round 17 up to 20 and 27 down to 25 for the approximation.
By doing so, we simplify the multiplication to 20 x 25.
The estimated product using compatible numbers would be:
20 x 25 = 500
So, an estimated answer to 17 x 27 using compatible numbers would be 500.
This method provides a quick and easy way to estimate the result, which is particularly useful when exact calculations are not necessary, or you need a fast approximation.
The function f(x) is shown in the graph. What is the equation for f(x)?
f(x)=____
Answers
express the equation in slope-intercept form: f(x) = mx + b.
Here's a general outline of the process we'll follow once I have the graph:
Identify key features:
Slope: Determine the slope of the line, which signifies the rate of change of the function. You can calculate it using the formula slope = (change in y) / (change in x) between any two points on the line.
Y-intercept: Locate the point where the line intersects the y-axis. This point is crucial for determining the function's vertical shift.
Apply slope-intercept form:
Once you have the slope (m) and y-intercept (b), express the equation in slope-intercept form: f(x) = mx + b.
Verify with points:
Choose a few points on the graph and substitute their coordinates into the equation to ensure it accurately represents the line.
Evaluate 2(10 - d) + f, when d = 7 and f = -3.
A. -2
B. 3
C. 9
D. 20
Answers
Answer:
B. 3
Step-by-step explanation:
2(10 - d) + f
d = 7 and f = -3
Substitute these value in
2(10 - 7) + -3
2 * (3) -3
6 -3
3
Put the values of d = 7 and f = -3 to the expression 2(10 - d) + f
Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
------------------------------------------------------------------------------
2(10 - 7) + (-3) = 2(3) - 3 = 6 - 3 = 3
Answer: B. 3The Pythagorean theorem, a^2+b^2=c^2, is used to calculate the side length of a right triangle. Which equation can be used to calculate the missing side length, b, of a right triangle?
Answers
Answer:
D b = sqrt(c^2 -a^2)
Step-by-step explanation:
We are using the Pythagorean theorem,
a^2+b^2=c^2
We want to solve for b
Subtract a^2 from each side
a^2 -a^2+b^2=c^2-a^2
b^2 = c^2 -a^2
Take the square root of each side
sqrt(b^2) = sqrt(c^2 -a^2)
b = sqrt(c^2 -a^2)
Answer:
answer A : b=√(c-a)
Step-by-step explanation:
a²+b²=c²
subtract a² from both sides to isolate b²
b²=c²-a²
take the square root of both sides to get from what b² equals to what b equals
b=√(c-a)
One quart or one liter? Which is greater?
Answers
1 liter = 1.06 quarts.
This makes the liter greater than a quart.
steve ran 15 miles in 2 hours what in his speed in miles per hour
Answers
Answer:
speed = 7.5 miles per hour
Step-by-step explanation:
To find the speed, we divide the distance by the time
speed = distance/time
speed = 15miles/2 hours
speed = 15/2 miles per hour
speed = 7.5 miles per hour
The location of four game stops are on a coordinate grid are as follows: Stop 1 at (−2,1) Stop 2 at (−2, −7) Stop 3 at (5,−7) Stop 4 at (5, 1) Paulo begins at Stop 1 and then walks to Stop 2, then Stop 3, and then Stop 4. Then he walks to Stop 1 again. The path between each stop is a straight line. One unit on the coordinate grid equals 125 feet. What is the total distance Paulo walked?
Answers
Answer:
3750 ft
Step-by-step explanation:
Denote Stops as points A(-2,1), B(-2,-7), C(5,-7) and D(5,1) and find all distances between two consecutive points:
[tex]AB=\sqrt{(-2-(-2))^2+(1-(-7))^2}=8\ units;[/tex][tex]BC=\sqrt{(-2-5)^2+(-7-(-7))^2}=7\ units;[/tex][tex]CD=\sqrt{(5-5)^2+(1-(-7))^2}=8\ units;[/tex][tex]DA=\sqrt{(5-(-2))^2+(1-1)^2}=7\ units.[/tex]The total distance Paolo walked is
[tex]8+7+8+7=30\ units.[/tex]
Since 1 unit on the coordinate grid equals 125 feet, then the total distance Paolo walked is
[tex]30\cdot 125=3750\ ft.[/tex]
you have a 20 ounce bottle of juice. you pour out 1/4 of the bottle to share with a friend. if your our out 3 ounces for yourself, what fraction of the 20 ounces will be left in the bottle?
Answers
Turn the 1/4 into a decimal which is 0.25 and times that by 20 and you’ll get 5, 5 is the amount of ounces you poured for your friend. Subtract 20 ounces by 5 ounces and you’ll get 15 ounces, then subtract 15 by 3 which is the amount of juice you poured for yourself and you’ll be left with 12 ounces in the bottle.
To determine the remaining fraction of juice in the bottle, subtract the poured amount from the original 20 ounces. The fraction left in the bottle is 3/5 of the original 20 ounces.
To find the fraction of juice left in the bottle:
Start with 20 ounces.
Pour out 1/4 for a friend, which is 5 ounces (1/4 of 20).
Pour out 3 more ounces for yourself.
Subtract the total poured out (5 + 3 = 8) from the starting amount (20) to find what's left.
So, 20 - 8 = 12 ounces left in the bottle, which represents 3/5 of the original 20 ounces.
John bought 6 dumplings for $3.00.
Let x represent the number of dumplings purchased, and let y represent the total cost.
Graph the line that represents the proportional relationship.
Line
Answers
2 dumplings,$4
3 dumplings,$6
4 dumplings,$8
5 dumplings,$10
Answer:
Step-by-step explanation:
The first dote should go on the 0 and the second dote should go on the two
In the number 668 the 6 in the hundreds place is _ the value of the 6 in the tens place
Answers
6 in the tens place =60
What is the negative x-intercept of the graph of the quadratic function f(x) = 5x2 + 4x - 1? A) - 7 5 B) - 2 5 C) - 1 5 Eliminate D) -1
Answers
Answer:
D
Step-by-step explanation:
The quadratic formula is
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. Using the formula will require less work than finding the factors if factorable. We will substitute a=5, b=4 and c=-1.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-4+/-\sqrt{(4)^2-4(5)(-1)} }{2(5)}\\x=\frac{-4+/-\sqrt{16+20} }{10}[/tex]
We will now simplify and solve.
[tex]x=\frac{-4+/-\sqrt{36}}{10}\\x=\frac{-4+/-6}{10}[/tex]
x=-1 and x=0.2
URGENT!!!!
LM is the mid segment of ABCD. AB=69 and DC=182. What is LM
Answers
Answer: 125.5 is the answer in decimal form. If you need it in fraction form it would be 251/2
To get this answer, you add up the parallel sides AB+DC = 69+182 =251
Then you divide by 2 leading us to get 251/2 = 125.5
The midsegment is basically the average of the two parallel sides
Maya wants to divide 3/4 pound box of trail into small bags. Each bag will hold 1/12 pound of trail mix. How many bags of trail mix can maya fill ?
Answers
Answer:
9 bags of trail mix
Step-by-step explanation:
I would take the fraction 3/4 and make it have a common denominator with 1/12. In order to do that, multiply each number in 3/4 by 3. It results in 9/12.
You can put 9 of 1/12 in 9/12
To find out the number of bags Maya can fill with 3/4 pound of trail mix, divide 3/4 by 1/12. The division equates to multiplication by the reciprocal, so (3/4) x (12/1) = 9. Therefore, Maya can fill 9 bags of trail mix.
Explanation:This problem can be solved by division. Maya has 3/4 pound of trail mix and each small bag holds 1/12 pound of trail mix. Therefore, divide 3/4 by 1/12 to find out exactly how many bags Maya can fill.
To perform this division, you could first convert the fractions to decimals or do it directly. But let's stick with fractions and apply the principle of multiplying by the reciprocal. Change the division to multiplication and multiply 3/4 by the reciprocal of 1/12.
(3/4) x (12/1) = 9
So, Maya can fill 9 bags of trail mix.
Learn more about Division of Fractions here:https://brainly.com/question/17205173
#SPJ3
Which of following statements are true? 1. -18>5 2. -5> 0.5 3. -5>. 0 4. -5 > 5squared 5. -5> -18
Answers
A negative number is always less than a positive number.
When comparing two negative numbers, the smaller negative number is the greater value.
The answer would be 5. -5 > -18
Answer:
5. -5 > -18
Step-by-step explanation:
Positive numbers are greater than negative ones. Also think of the numbers on a mercury thermometer :- -5 his greater ( and warmer!) than -18.
Select Independent or Not independent for each pair of events.
Rolling a 1 on a number cube and then rolling a 6 on the same number cube
Flipping heads on a coin flip and then spinning an odd number on a spinner
Selecting a quarter from a bag of coins, putting it in a parking meter, and then selecting a dime from the same bag
Answers
Answer:
The first pair of events are independent, the second pair of events are independent and the third pair of events are dependent.
Step-by-step explanation:
Independent events are events that do NOT rely on previous events. So, the chances of each of event happening in a pair of events is independent, or has no effect, on the chances of the other event. In the case of rolling a number cube and then rolling it again, your chances would be the same each time you roll the number cube as to what number you would get. Just because you rolled a '1' on the first roll, doesn't mean you can't get the same number (or another number) on another roll. The same reasoning applies to the coin flip and the spinner. These two events are not related and in no way would rely on each other. A coin flip will not affect the chances of spinning an odd number. However, if we have several coins in a bag and select a quarter, but do not replace it, our chances of selecting another coin changes because there are not only less coins in the bag, but there are less quarters to choose from. In the case of events with NO replacement, these events are dependent.
Maria deposited some money in to an account, and had an annual simple interest rate of 5%. If she left the money in the account for 9 months and earned $18.75 in interest, how much money did she originally deposit into the account?
Answers
Answer:
$18.71
Step-by-step explanation:
18.75 = P x .05 x .75
18.75 = P x .0375
18.75 - .0375 = P
$18.71 = P
CAN SOMEONE PLS HELP!???
Answers
Answer: 10%, 0.5, 3/4
Step-by-step explanation:
What you want to do is convert them all to one unit. The eaisest would be a decimal.
Starting off with .5, it's already in decimal form.
Next go to 10%. 10% as a decimal will be 0.1, because its 1/10.
Lastly, go to 3/4. 3/5 as a decimal would be 0.75.
Putting them in order from least to greatest would be 10%, 0.5, 3/4.
(Hope that helps)
Answer:
10%, 0.5, 3/4
Step-by-step explanation:
This is actually quite simple, all you need is a quick calculation.
I'm going to convert all of the numbers to decimals for the easiest comparison.
put 3/4 into a calculator, and you get 0.75
0.5 is already a decimal
and with percents, you just move the decimal point back two, making it 0.1
Now you have an easy way to compare: 0.1 is the least, 0.5 is next, the 0.75 is the largest.
Hope this helps =D
Circle A has a radius of 6. Which circles are congruent to circle A? Check all that apply. circle D circle E circle F circle G circle H
Answers
Answer:
circle E & circle F
Step-by-step explanation:
We want to see which circles are congruent to circle A, a circle of radius of 6 units.
The correct options are E and F.
Let's see how to solve this:
First, we need to understand what congruent figures are.
We say that two figures are congruent if they have the exact same shape and size.
Then we need to see which other circles also have a radius (distance from the center to the line) is also of 6 units. (or a diameter of 12 units)
The image of the options can be seen at the end of the answer, there, we can see that circle E has a radius of 6 units, so we know that circle E is congruent to circle A.
We also can see that circle F has a diameter (twice the radius) of 12 units, then the radius is:
R = D/2 = 12/2 = 6 units.
Then circle F is also congruent to circle A.
Then the correct options are E and F.
If you want to learn more, you can read:
https://brainly.com/question/12132062
What is the greatest number of pairs of shoes sold in 1 week?
Answers
Answer:
30
Step-by-step explanation:
Answer:
It is 50,000
Step-by-step explanation:
What’s the answer show your WORK Plz
Answers
Answer:
732.7 I think
Step-by-step explanation:
You just multiply 28 by 26.17
Answer:
26.17*28=723.76 inches
Why?
There is 28 desks and they are 26.17 inches long. If you line them all up you have 28 desks each 26.17 inches in a line. Which is 26.17*28. Multiple and you get 723.76
It cost six dollars Per pound of peanuts at Blessed Food Market. Which of the following represents The range of the function in terms of cost per pound?
A. $6
B. Amount of peanuts
C. Cost of peanuts purchased
D. Peanuts purchased
Answers
Answer:
C. Cost of peanuts purchased
Step-by-step explanation:
The range is the values that the y variable, or the output can take.
The output is the cost of the peanuts
When Tom purchased a new motorcycle, he paid a 5% sales tax. The amount of sales tax he paid was $265. What was the total cost of the motorcycle including the sales tax? Enter your answer in the box. $
Answers
Tax (5.0%) : $ 265.00
Gross Amount (including tax) : $5,565.00
Math:
[tex]5300.00 \times .05 = 265.00[/tex]
[tex]5300.00 + 265.00 = 5565.00[/tex]
8. Workpad Note: Remember to show all of the steps you use to solve a problem. You can use the comments field to explain your work. Your teacher will review each step of your response to ensure yiu recieve proper credit for your answer.
At the half-time show, a marching band marched in formation. The lead drummer started at a point with coordinates (2,-5) and moved 3 steps up and 1 step right.
a. Write a rule to describe the translation.
b. what were the coordinates of the drummer's final position?
Answers
(2,-5) (3,-3)
Answer: a) (x, y) → (x + 1, y + 3)
b) (2, -5) → (3, -2)
Step-by-step explanation:
the x-axis goes left and right, so 1 step to the right means you need to add 1 unit to the x-coordinate.
the y-axis goes up and down, so 3 steps up means you need to add 3 units to the y-coordinate.
Rule:
If original x-coordinate is x, then the new coordinate is x + 1 (x → x+1)
If original y-coordinate is y, then the new coordinate is y + 3 (y → y+3)
Final position:
If original x-coordinate is 2, then the new coordinate is 2 + 1 (2 → 3)
If original y-coordinate is -5, then the new coordinate is -5 + 3 (-5 → -2)
choose the correct solution set for each graph
Answers
1. The range of the Domain: x I x ≤ -2
2. The range of the Domain: (-5, ∞)
3. The range of the Domain: (-2, 3)
Leftmost Graph:
Domain: x I x ≤ -2
Range: All real numbers (-∞, ∞)
Visual: A solid line extending infinitely to the left from a closed circle at -2, indicating all values less than or equal to -2.
Interpretation: Includes -2 and all numbers to its left (negative infinity).
Middle Graph:
Domain: (-5, ∞)
Range: All real numbers (-∞, ∞)
Visual: A solid line starting with an open circle at -5 and extending infinitely to the right, indicating all values greater than -5.
Interpretation: Includes all numbers greater than -5, but not -5 itself.
Rightmost Graph:
Domain: (-2, 3)
Range: All real numbers (-∞, ∞)
Visual: A solid line between open circles at -2 and 3, indicating values between those points but not including those endpoints.
Interpretation: Includes all numbers strictly between -2 and 3, but not -2 or 3 themselves.
Answer: attachment
Step-by-step explanation:
Noah wants to put a varitey of fish in his new tank his tank is large enough to hold 70 fish find how many fish of each breed he can have 20% are raibbow 40% are swordtail molly are 30%
Answers
The amounts of each type of fish that Noah is going to have in his tank are given as follows:
14 raibbow.28 swordtail molly.21 of the remaining.How to obtain the amounts?The quantity of each type of the fish listed in this problem that Noah will have in his tank is obtained applying the proportions in the context of the problem.
The total capacity of the tank is of 70 fish, hence for the amounts of each fish we multiply 70 by the decimal equivalent to each percentage.
Applying the proportions, the amounts are given as follows:
14 raibbow, as 0.2 x 70 = 14.28 swordtail molly, as 0.4 x 70 = 28.21 of the remaining, as 0.3 x 70 = 21.More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
please help i really need help
Answers
Help me again, please. ;w;
Answers
5x - 7y =58
y =-x +2
Using the substitution method, replace y in the first equation with the second equation:
5x - 7(-x+2) = 58
Simplify by using the distribution property:
5x - (-7x) - 14 = 58
Simplify by combining like terms:
12x -14 = 58
Add 14 from each side of the equation:
12x = 72
Divide both sides by 12:
X = 72/12
x = 6
Now you have x, replace x in the second equation and solve for y:
y = -x +2
y = -6 +2
y = -4
X = 6, y = -4