Question

The graph of an absolute value function f(x) = a|x| includes the point (1, 8). Complete the following statements.Another point on the graph is ( ?, 8).The value of a is

Answer 1

`f(x)=a\lvert x\rvert`

In a absolute value graph the value of y is the same in -x and x.

Then if the coordinates (x,y) one point is (1, 8), the graph have another point in (- 1, 8).

To find the value of a you use one of the points (x,y) in the general form of absolute value:

( 1 , 8) x=1 f(x)= y=8

`8=a\lvert1\rvert`

As:

`\lvert\pm a\rvert=a`

You get:

`8=a\cdot1`

Then:

`a=8`

The equation for the graph with points (1 , 8) and ( -1, 8) is:

`f(x)=8\lvert x\rvert`a= 8