What is the effect on the graph of the parent function f (x) = x when f (x) is replaced with f (9x) ?

A) shifts the line 9 units left

B) shifts the line 9 units right

C) increases the slope of the line by a factor of 9

D) decreases the slope of the line by a factor of 9

Answer:c

Step-by-step explanation:c

option: C is correct.

Step-by-step explanation:

since, we are given a parent function f (x) as: f (x) = x.

We are asked to find what change will occur in the function when the parent function f (x) is replaced by f (9x).

let g (x) be the function formed by replacing f (x) with f (9x) i. e.

g (x) = f (9x) = 9x.

clearly the slope of the function g (x) = f (9x) is 9. (since on comparing the equation with the slope intercept form y=mx+c; where m is the slope of the line and c is the y - intercept).

whereas the slope of the function f (x) = x is 1.

Hence there is an increment of slope by a factor of 9.

Hence, option C is correct.