IDNLearn.com is your go-to platform for finding accurate and reliable answers. Ask any question and receive comprehensive, well-informed responses from our dedicated team of experts.
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
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.
