Question

Given the coordinates for the function below, which of the following arecoordinates for its inverse?Gallons Cost, inof Gas Dollars125151.252.506.2518.7525.0020

Answer 1

Given the coordinates for the function:

Gallons of gas Cost, in Dollars

1 1.25

2 2.50

5 6.25

15 18.25

25 25.00

Let's find the coorddinates of the inverse.

To find the coordinats of the inverse, let's find the original function.

Apply the slope-intercept form of a linear function:

y = mx + b

Where m is the rate of change and b is the y-intercept.

To find the rate of change, we have:

`y=(y2-y1)/(x2-x1)=(2.50-1.25)/(2-1)=(1.25)/(1)=1.25`

To solve for b, we have:

`\begin{gathered} y=1.25x+b \\ \\ 1.25=1.25(1)+b \\ \\ 1.25=1.25+b \\ \\ b=1.25-1.25=0 \end{gathered}`

The function for the given table is:

y = 1.25x

To find the inverse of the function, let's interchange the variables:

`x=1.25y`

Solve for y:

Divide both sides by 1.25

`\begin{gathered} (x)/(1.25)=(1.25y)/(1.25) \\ \\ (1)/(1.25)x=y \\ \\ 0.8x=y \\ \\ y=0.8x \end{gathered}`

Therefore, the inverse of the function is:

y = 0.8x

Let's find the coordinates of the inverse function.

When x = 1:

`y=0.8(1)=0.8`

When x = 2:

`y=0.8(2)=1.6`

When x = 3:

`y=0.8(3)=2.4`

When x = 4:

`y=0.8(4)=3.2`

When x = 5:

`y=0.8(5)=4.0`

Therefore, the coordinates for the inverse function are:

Gallons of Gas Cost in dollars

1 0.8

2 1.6

3 2.4

4 3.2

5 4.0

ANSWER:

Gallons of Gas Cost in dollars

1 0.8

2 1.6

3 2.4

4 3.2

5 4.0