Question

What is the effect on the graph of the function f(x) = 2x when f(x) is changed to f(3x)?

A)
vertical stretching


B)
vertical compression


C)
horizontal compression


D)
horizontal stretching

Answer 1

C) Horizontal compression

Explanation:

Since, if y = f(x) is a function,

Then y = a f(x) gives a vertical stretch if a > 1 and gives a vertical compression if 0 < a < 1.

Also, y = f(bx) gives a horizontal stretch when 0 < b < 1 and gives a horizontal compression if b > 1.

Here,

The given parent function is,

f(x) = 2x

And, 3 > 1

Thus, by the above statements,

f(3x) will give a horizontal compression.

Hence, Option C is correct.