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Sagot :
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:
[tex]y=\frac{y2-y1}{x2-x1}=\frac{2.50-1.25}{2-1}=\frac{1.25}{1}=1.25[/tex]To solve for b, we have:
[tex]\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}[/tex]The function for the given table is:
y = 1.25x
To find the inverse of the function, let's interchange the variables:
[tex]x=1.25y[/tex]Solve for y:
Divide both sides by 1.25
[tex]\begin{gathered} \frac{x}{1.25}=\frac{1.25y}{1.25} \\ \\ \frac{1}{1.25}x=y \\ \\ 0.8x=y \\ \\ y=0.8x \end{gathered}[/tex]Therefore, the inverse of the function is:
y = 0.8x
Let's find the coordinates of the inverse function.
When x = 1:
[tex]y=0.8(1)=0.8[/tex]When x = 2:
[tex]y=0.8(2)=1.6[/tex]When x = 3:
[tex]y=0.8(3)=2.4[/tex]When x = 4:
[tex]y=0.8(4)=3.2[/tex]When x = 5:
[tex]y=0.8(5)=4.0[/tex]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
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