how do you graph the inverse function of f(x)=1/2x-5 ?

Question

this is for IM2 math honors i need help on this i understand the switching part i just need an example to help me continue my homework.

Answer 1

Let y=f(x). Therefore, y=(1/2)x-5 which is a line of slope 1/2 and y-intercept of -5. The inverse function of this equation will also be a line. We find this by switching the x & y then solve for y:

                  y=(1/2)x-5                original equation

                  x=(1/2)y-5                switch x & y

                  x+5=(1/2)y               isolate the y term by adding 5 to each side

                 2(x+5)=y                   multiply both sides by 2 to isolate y

                 2x+5=y                     the inverse function

The inverse function is a line with slope of 2 and y-intercept of 5. If you were to plot both functions on the same graph you would see that the 2 functions are symmetrical about the line y=x.

Answer 2

y= (1/2)X - 5

 

x = (1/2)y - 5

 

x+5 = (1/2)y

 

2(x+5) = y

 

2x + 10 = y

 

slope is 2; y-intercept is (0,10)

 

Starts at (0,10); go up two and over 1, so (1,12)