Question

Which statement correctly describes the graph of G(x) = -3f(x)?

A. The graph of g is the graph of f horizontally stretched by a scale factor of 3 and reflected over the x-axis

B. The graph of g is the graph of f horizontally stretched by a scale factor of 3 and replicated over the y-axis

C. The graph of g is the graph of f vertically stretched by a scale factor of 3 and reflected over the x-axis

D. The graph of g is the graph of f vertically stretched by a scale factor of 3 and reflected over the y-axis

Answer 1

Answer:

C is the correct choice.

Step-by-step explanation:

Here are the rules for vertical stretches and reflection

Given a function f(x), a new function $g(x)= a \cdot f(x),$ where a is a constant, is a vertical stretch or vertical compression of the function f(x).

• If a>1, then the graph will be stretched vertically

• If 0<a<1, then the graph will be compressed vertically

• If a<0, then there will be combination of a vertical stretch or compression with a vertical reflection around the x-axis

Since the question use a multiplicative of -3, and -3 < 0 we get the correct choice as C: The graph of g is the graph of f vertically stretched by a scale factor of 3 and reflected over the x-axis