Question

Suppose f(x) = x2 and g(x) = 7x2. 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 stretched by a factor of 7.
B. The graph of g(x) is the graph of f(x) shifted 7 units up.
C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 7.
D. The graph of g(x) is the graph of f(x) vertically compressed by a factor of 7.

Answer 1

Therefore, The correct option is A. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 7.

Explanation:

For better explanation of the solution see the attached graphs of both the given functions :

The function f(x) is given to be : f(x) = x²

This is an equation of parabola open vertically upwards

The function of g(x) is given to be : g(x) = 7x²

This is also equation of the parabola open vertically upwards

Now, g(x) = 7x²

⇒ g(x) = 7 × x²

⇒ g(x) = 7 × f(x)

So, the graph of the function g(x) is vertically stretched by the factor of 7 as compared to that of the graph of the function f(x)

Therefore, The correct option is A. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 7.

Answer 2

The graph of g(x) is the graph of f(x) vertically stretched by a factor of 7.