The graphs below have the same shape. The equation of the blue graph is f(x) = 2x. Which of these is the equation of the red graph, g(x)?
Answers
As we can see, the graphs look identical in every way except that g(x) is lower than f(x).
This means that the graph is shifted down a certain amount.
If we look at the y-intercepts of the two functions, we see that f(x) has a y-intercept of 1, and g(x) has a y-intercept of -1.
This means that f(x) is two units lower than g(x).
The y-intercept of a function can be changed by adding or subtracting a number to the original function (in this case 2^{x}).
Because the graph f(x) is 2 lower than the graph of g(x), we can find g(x) by subtracting 2 from f(x).
Therefore, g(x) = 2^{x} - 2.
The functions f(x)=x² and g(s)=s² are essentially the same function with different variable notations. The f(x)=2x graph is linear, and the red graph g(x) with the same shape would also be linear, involving a transformation that retains the proportional relationship between x and y.
Explanation:Based on the provided information, the equation of f(x) is given as f(x) = x². If the blue graph represents this function, and we are looking for the red graph equation g(x), which has the same shape, we need to understand the transformation involved.
Regarding the equations provided in the examples, functions f and g are both defined as taking an input, squaring it, and outputting the result. Although they use different variable names (x for f and s for g), they are effectively the same function. When you have a transformation such as f(x-2), the graph of the function shifts to the right without changing its shape. Similarly, if the red graph were g(x) = 2x, the transformation applied would be to double the output, stretching the graph vertically relative to f(x).
Since the blue graph equation is given as f(x) = 2x and the red graph has the same shape, it means the red graph, g(x), also has a linear relation with a proportional transformation applied. Common linear transformations include multiplying by a scalar to scale the graph or adding/subtracting a number to shift the graph along the x-axis or y-axis.
Related Questions
Mick has a bag with 2 mint sticks, 11 jelly treats, and 7 fruit tart chews. If he eats one piece every 10 minutes, what is the probability his first two pieces will be a jelly treat and a mint stick?
Give your answer in a percent.
Answers
To find the probability, calculate the probabilities of selecting a jelly treat and a mint stick. Then multiply these probabilities together to find the overall probability.
Explanation:To find the probability that Mick's first two pieces will be a jelly treat and a mint stick, we need to calculate the probability of selecting a jelly treat and a mint stick from the bag.
First, we need to find the total number of pieces in the bag: 2 mint sticks + 11 jelly treats + 7 fruit tart chews = 20 pieces.
The probability of selecting a jelly treat as the first piece is: 11 jelly treats / 20 total pieces = 0.55 or 55%.
After Mick has eaten one piece, there are now 19 pieces left in the bag.
The probability of selecting a mint stick as the second piece is: 2 mint sticks / 19 remaining pieces = 0.105 or 10.5%.
Therefore, the probability that Mick's first two pieces will be a jelly treat and a mint stick is 55% * 10.5% = 0.055 or 5.5%.
You are making balloon arrangements for a birthday party. there are 16 white balloons and 24 red balloons. each arrangement must be identical. what is the greatest number of arrangements you can make using every balloon?
Answers
This is basically a GCF problem. To find the
GCF, we list the factors of each number.
24 = 1×24, 2×12,
4×6, 8×3 ...
16 = 1×16, 2×8,
4×4, ...
The greatest common factor is 8 because it is the greatest
factor we can find.
So 8 arrangements
a 12-ft-by-15-ft swimming pool has a 3-ft-wide no-slip surface around it. what is the outer perimeter of the no-slip surface?
Answers
see diagram
we see we doulbe the 3 to add
3*2=6
6+12=18
6+15=21
thelength and width of the surfface is 18 by 21
P=2(L+W)
P=2(21+18)
P=2(39)
P=78
the perimiter is 78ft
Answer:
A
Step-by-step explanation:
78 ft
How do I solve this ?
Answers
2. n=5
CHECK MY ANSWERS IN CASE I MADE A MISTAKE
3*4=2x
12=2x
6=x
Final answer: x=6
P and q are on a number line. If p has a coordinate -5 and pq =7 , what could the coordinate of p be
Answers
Given quadrilateral jklm with diagonals that bisect the vertices, what kind of quadrilateral is jklm? rhombus parallelogram trapezoid generic quadrilateral (no more specific classification can be determined)
Answers
An equation with an exponent is called an exponential equation. true or false?
Answers
11+22+33+...+1010 is divided by 5. what is the remainder? (a) 0 (b) 1 (c) 2 (d) 3 (e) 4
Answers
so the sum will end in 5 so its divisible by 5 and the remainder will be 0
It (a)
Math Quiz Question! Measuring segments and Angles
In the diagram, m < ACB = 65
m < BCD =
Answers
180-65= 115=<BCD
What is the value of y?
Enter your answer in the box.
Answers
Let's start off by writing an equation representing the sum of the interior angles of the given triangle.
y+79+37=180
Now, let's solve the equation for the variable 'y'.
y+79+37=180
Combine like terms:
y+116=180
Subtract 116 from both sides of the equation:
y+116-116=180-116
y=64
The measure of angle y is 64 degrees.
When functions are defined by more than one equation, they are called?
Answers
When functions are defined by more than one equation, they are called Piecewise defined functions.
What is Piecewise- defined function?
A Piecewise defined function is one which is defined not by a single equation, but by two or more.
Hence,
When functions are defined by more than one equation, they are called Piecewise defined functions.
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Joe earns $10 per hour babysitting and $5 per hour dog walking. He also earns tips for each job. Last week Joe spent 6 more hours walking dogs than babysitting. He received $5 in tips for babysitting and $10 in tips for dog-walking. Joe earns the same total amount for each job. Write an equation to represent the situation. Use the variable H to represent the number of hours Joe spent babysitting.
Answers
10h + 5 = 5h + 30 +10
10h-5h = 30 +10 -5
5h = 35
h=7
Answer:
54
Step-by-step explanation:
25. What is (2.5 X 102)(6.3 X 105) in scientific notation? Show all your work below
a. 1.575 X 107
b. 1.575 X 106
c. 1.575 X 1010
d. 1.575 X 108
Answers
___________________________________________________
The problem is:
___________________________________________________
"What is: "(2.5 * 10²) (6.3 * 10⁵)" (in scientific notation)?
___________________________________________________
(2.5 * 10²) (6.3 * 10⁵) =
2.5 * 10² * 6.3 * 10⁵ =
2.5 * 6.3 * 10² * 10⁵
= 2.5 * 6.3 * 10⁽² ⁺ ⁵) =
= 2.5 * 6.3 * 10⁷ ;
______________________________________________________
Note the following property of exponents:
______________________________________________________
xᵃ * xᵇ = x ⁽ᵃ ⁺ ᵇ⁾ ;
______________________________________________________
Thus: 10² * 10⁵ = 10⁽² ⁺ ⁵) = 10⁷ ;
______________________________________________________
So; we have:
______________________________________________________
2.5 * 6.3 * 10⁷ ;
→ 2.5 * 6.3 * 10⁷ = (2.5 * 6.3) * 10⁷ = 15.75 * 10⁷ .
______________________________________________________
The answer is: [A]: " 15.75 * 10⁷ " .
______________________________________________________
24 loaves of bread cost $48. How much do 10 loaves cost
Answers
for 10 loaves...
2 * 10 = $ 20 <===
t−12/2=3/t2−3
solve for T
–3
–1
1
3
Answers
The answer is 3.
In the expression 4^9 the number 9 is called the
Answers
Hope this helps
please help me find the perimeter of this triangle please
Answers
add the sides with 8 and 6 to it, and that's the perimeter.
Is the following definition of perpendicular reversible? If yes, write it as a true biconditional. Two lines that intersect at right angles are perpendicular.
A. The statement is not reversible.
B. Yes; if two lines intersect at right angles, then they are perpendicular.
C. Yes; if two lines are perpendicular, then they intersect at right angles.
D. Yes; two lines intersect at right angles if (and only if) they are perpendicular.
Answers
Sarah has a job at a salon and she earns $50 per day plus tips. Her average tip is 15% of the total amount her customers spend on services. Sarah's daily income is represented by the variable y and the amount her customers spend is represented by the variable x. Which equation represents Sarah's daily income?
Answers
There are between 50 and 60 eggs in a basket. When Mohammed counts by 3's, there are 2 eggs left over. When he counts by 5's there are 4 left over. How many eggs are there in the basket?
Answers
3 : 48, 51, 54, 57, 60
5: 50, 55, 60
Choose a number that satisfies both:
59
When divided by 3 it has a remainder of 2
When divided by 5 it has a remainder of 4.
There are 59 eggs in the basket.
Hope This Helps You!
Good Luck :)
The correct answer is:
59
Explanation:
The numbers between 50 and 60 that are divisible by 3 are
51, 54, 57, 60
The numbers between 50 and 60 that are divisible by 5 are
50, 55, 60
We know that when he counts by 3s, he has 2 left over; this means the number he counts to is 2 fewer than the number of eggs. This means, counting by 3s, we could have
51+2, 54+2, 57+2, or 60+2 = 53, 56, 59, 62
62 is not an option, since we know we have between 50 and 60 eggs; this gives us 53, 56 or 59.
We also know that when he counts by 5s, he has 4 left over; this means the number he counts to is 4 fewer than the number of eggs. This means, counting by 5s, we could have
50+4, 55+4, 60+4, or 54, 59, 64
64 is not an option, since we know we have between 50 and 60 eggs; this gives us 54 or 59.
The only number in both lists is 59, so this must be the answer.
Tony will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $60 and costs an additional $0.30 per mile driven. The second plan has no initial fee but costs $0.80 per mile driven. How many miles would Tony need to drive for the two plans to cost the same?
Answers
The first car has a cost that can be calculated as a function of the miles driven:
f(m) = 60 + 0.3m
The second has a similar comportment:
s(m) = 0.8m
We want f(m) = s(m).
60 + 0.3m = 0.8m
0.8m - 0.3m = 60
0.5m = 60
m = 60 / 0.5
m = 120.
Tony would need to drive 120 miles to pay the same amount.
What is the equation of the line that is parallel to the given line and passes through the point (−4,−6 )?
A. x = −6
B. x = −4
C. y = −6
D. y = −4
Answers
we know that
The given line is parallel to the x-axis
so
the equation of the line that is parallel to the given line and passes through the point [tex](-4,-6 )[/tex] will be equal to the y-coordinate of the point
The y-coordinate of the point is [tex]-6[/tex]
therefore
the equation is
[tex]y=-6[/tex]
the answer is the option C
[tex]y=-6[/tex]
If |x| = 6 then x = -6 or
Answers
Remember that absolute value is the distance from the number and 0 on a number line.
Final answer: x=-6 or x=6
True or false: it is possible to determine a vector if only one of its components is known.
Answers
50 POINTS! PLEASE HELP!
Which of the binomials below is a factor of this trinomial? x2 - 3x - 4
A. x2 + 4
B. x + 4
C. x - 4
D. x + 8
Answers
x -4
x 1
(x-4) (x + 1)
your answer is C.x - 4
hope this helps
Answer:
c) x - 4
Step-by-step explanation:
To do a factorization of this kind of trinomial there is a technique very easy to do it.
First, you need to see the numbers that are along with the x and the independent number.
In this case -3 and -4 (I will call them b and c)
Next, you need to think in two numbers that can acomplish the following:
x * y = c
x + y = b
So, first, think, which are two numbers that you can multiply between them to give as a result -4?.
In this case it would be -4 and 1 (-4*1 = -4)
These numbers if you do a sum you'll get -3:
-4 + 1 = -3
So the factorization becomes this:
(x - 4) (x - 1)
So, one of the factors is x - 4. Option c
Harry buys a sofa set that costs $2000.00. He pays for it by installments at an interest rate of 5% per year. What is the total amount he has to pay at the end of the one year?
Answers
? = 105%
To calculate~~~~
[tex] \frac{2000}{100} [/tex] X 105
= $2100.00
Harry is required to pay an additional $100 as interest for one year on the $2000 sofa, bringing the total payment to $2100 at the end of the year.
Harry buys a sofa set at a cost of $2000 with an installment plan that includes an interest rate of 5% per annum. To calculate the total amount Harry needs to pay at the end of one year, you need to calculate the interest and then add it to the principal amount.
The interest for one year is calculated as follows:
Interest = Principal imes Rate imes Time.
Interest = $2000 imes 5% imes 1 year.
Interest = $2000 imes 0.05 imes 1.
Interest = $100.
Now, we add the interest to the principal amount to find the total amount Harry has to pay by the end of the year:
Total Amount = Principal + Interest.
Total Amount = $2000 + $100.
Total Amount = $2100.
Therefore, Harry will have to pay a total of $2100 at the end of one year.
Evaluate the function for x = m/4
f(x) = 8x^2 - 4x
A. 2m^2 - m
B. m^2 - m
C. m^2/2 - 4m
D. m^2/2 - m
Answers
Final answer:
To evaluate the function for x = m/4, substitute m/4 for x in the function[tex]f(x) = 8x^2 - 4x[/tex]and simplify to get the result [tex]m^2/2 - m.[/tex]
Explanation:
To evaluate the function [tex]f(x) = 8x^2 - 4x[/tex] for x = m/4, we substitute m/4 for x in the function and simplify.
Substitute x with m/4:
[tex]f(m/4) = 8(m/4)^2 - 4(m/4)[/tex]
Simplify the equation:
[tex]f(m/4) = 8(m^2/16) - m[/tex]
[tex]f(m/4) = (8/16)m^2 - m[/tex]
[tex]f(m/4) = m^2/2 - m[/tex]
Therefore, the correct answer is D. [tex]m^2/2 - m.[/tex]
The sum of two numbers is 180. One number is 5 times the other.
Answers
x +5x =18
6x =180
x = 180/6 = 30
1 number is 30
2nd number is 5*30 = 150
The elevation of Death Valley-282 feet. The Mississippi River in Illinois has an elevation of 279 feet. Which is closer to sea level?
Answers
death valley : | -282 | = 282....so this is 282 spaces from 0
mississippi river : | 279 | = 279...so this is 279 spaces from 0
so the mississippi river is closer to 0 then death valley
The Mississippi River is closer to sea level.
What is the length?It is the measure of distance between the two points called length.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The elevation of Death Valley is 282 feet.
The Mississippi River in Illinois has an elevation of 279 feet.
If the length of the elevation of Death Valley 282 is greater than the length of the Mississippi River 279.
The Mississippi River is closer to sea level.
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Use the data from the following chart to answer the question below.
it was 1.0 that was water this is what i have g/cm3
According to the chart, one milliliter of water would have a density of _____.
100 g/cm 3
10 g/cm 3
1 g/cm 3
cannot be determined
Answers
The density of water should be 1g/cm3. If you want to know how much it is in a milliliter, then you need to convert the cm3 into the milliliters. But the question is about density. The density of water will not be changed if its volume became less. The volume only used to determine the water weight. In this case, 1 milliliter of water will weight: 1ml * 1g/cm3 * 1cm3/ml= 1 gram
Answer:
1 g/cm 3
Step-by-step explanation: