Question

Given that (3,5) is on the graph of f(x) find the corresponding point for the function -3f(x)

Answer 1

(6,5)

Explanation:

This is a translation in the x-direction, so add 3 to the x-value. The y-value stays the same.

Answer 2

The point corresponding to (3,5) on the graph of the function -3f(x) is (-9,-15).

Explanation:

Since, we are given a function f(x) such that the point (3,5) lie on the graph of the function f(x).

Now we are given a new function g(x) as -3f(x) i.e. g(x)=-3f(x).

Clearly this new function g(x) is a dilation of f(x) by a scale factor of '-3'.

Hence every coordinates of the this new function will get multiplied by the scale factor.

i.e. (-3×3,-3×5)=(-9,-15)

Hence, the point corresponding to the point (3,5) on the graph of f(x) will convert to the point (-9,-15) on the graph of g(x)= -3f(x).