Question

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

A) stretched vertically
B) compressed vertically
C) stretched horizontally
D) compressed horizontally

Answer 1

The graph is compressed vertically.

Explanation:

The parent function is f(x) = |x|.

Now, some of the solution of this function are

At x = 0, f(x) = 0

At x = 1, f(x) = 1

At x = 2, f(x) = 2

At x = - 1, f(x) = 1

Now, if we replace, f(x) by 3f(x), then we get the equation
`f(x) = (1)/(3) |x|`.

Now, the few solutions of the function are

At x = 0, f(x) = 0

At x = 1,
`f(x) = (1)/(3)`

At x = 2,
`f(x) = (2)/(3)`

At x = - 1,
`f(x) = (1)/(3)`

Therefore, the f(x) values are reduced by the factor
`(1)/(3)`.

So, the graph is compressed vertically. (Answer)

Answer 2

a) Stretched vertically.

Explanation:

The product of a function and a real number greater than 1 mean that resultant function is stretched vertically.