Question

Find the ordered pairs of the inverse function. Graph the function and its inverse.

Answer 1

The equation of a line is given as:

y = mx + c

Let us get the eqiuations for the first two sets of data points

( 1, 5) and (2, 2)

For (1, 5), the equation becomes:

5 = m + c

m + c = 5........(1)

For (2, 2), the equation becomes:

2 = 2m + c

2m + c = 2........(2)

Subtract equation (1) from (2)

m = -3

Put the value of m into equation (1) to get the value of c

-3 + c = 5

c = 5 + 3

c = 8

The general equation then becomes:

y = -3x + 8

To confirm that this function is right, put the third data point into the equation and see if it is true.

(3, -1)

-1 = -3(3) + 8

-1 = -9 + 8

-1 = -1 (true)

To find the inverse of the function y = -3x + 8

Make x the subject of the formula

-3x = y - 8

`\begin{gathered} \text{x = }(-(y-8))/(3) \\ \text{x = }(-y+8)/(3) \end{gathered}`

To get the inverse function, replace x by y, and vice-versa

`y\text{ = }(-x+8)/(3)`

We will now use the values of y in the first table as x in the inverse function table:

when x = 5

y = (-5 + 8)/3

y = 3/3, y = 1

When x = 2

y = (-2 + 8)/3 = 6/3

y = 2

When x = -1

y = (-(-1) + 8) / 3 = (1 + 8)/3

y = 9 / 3

y = 3

The table for the inverse function is therefore:

Below is the graph for the original function:Below is the graph for the inverse function: