Question

Which statement about the relationship between the graph of the quadratic parent function, f(x) = x2 , and the function, g(x) = 2x2 + 5, is true? The graph of g(x) is narrower than the graph of f(x) and translated up five units. The graph of g(x) is narrower than the graph of f(x) and translated down five units. The graph of g(x) is wider than the graph of f(x) and translated up five units. The graph of g(x) is wider than the graph of f(x) and translated down five units.

Answer 1

Answer:

A) The graph of g(x) is narrower than the graph of f(x) and translated up five units.

Step-by-step explanation:

First, we can define g(x) in terms of f(x) by:

• substituting f(x) = x²

↓↓↓

g(x) = 2 f(x) + 5

In this form of g(x), we can see how it transforms, or changes, f(x).

• It is multiplied by 2, which is > 1, so f(x) is being stretched vertically. We can also call this being narrowed.

• 5 is added to it, so it is shifted up 5 units.

Thus, the statement that describes the relationship between f(x) and g(x) is:

A) The graph of g(x) is narrower than the graph of f(x) and translated up five units.