Question

Suppose f(x) = x2 and g(x) = 4x2. Which statement best compares the graph of g(x) with the graph of f(x)?


A. The graph of g(x) is the graph of f(x) vertically compressed by a factor of 4.
B. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.
C. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 4.
D. The graph of g(x) is the graph of f(x) shifted 4 units left.

Answer 1

Given:
f(x) = x²
g(x) = 4x²

Therefore
g(x) = 4f(x)
This means that the value of g(x) is 4 times the value of f(x). So the graph og (x) is the graph of f(x) vertically stretched by a factor of 4.

The graph shown below confirms the conclusion.

Answer: C.
The graph of g(x) is the graph of f(x) vertically stretched by a factor of 4.