Question

What is the effect on the graph of f(x) = |x| when the function is changed to g(x) = |3x| + 1?

A) The graph of g(x) is shifted 1 unit up.
B) The graph of g(x) is shifted 1 unit down.
C) The graph of g(x) is stretched horizontally by a factor of 3.
D) The graph of g(x) is compressed horizontally by a factor of 3.

Answer 1

The graph of g(x) = |3x| + 1 is obtained by stretching the graph of f(x) = |x| horizontally by a factor of 3 and shifting it 1 unit up. Hence, A) is correct.

Step-by-step explanation:

The graph of the function g(x) = |3x| + 1 is obtained by stretching the graph of the function f(x) = |x| horizontally by a factor of 3 and shifting it 1 unit up.

The original function f(x) = |x| has a V-shape, where the vertex is at the origin (0, 0). By multiplying the x-coordinates by 3, the graph is stretched horizontally, making the vertex at (0, 0) expands to (0, 1). Then, by shifting the graph 1 unit up, the vertex is now at (0, 1).

Therefore, the effect on the graph of f(x) = |x| when it is changed to g(x) = |3x| + 1 is that the graph of g(x) is shifted 1 unit up.