Question

Select the options from the drop down menus to complete each sentence

Answer 1

The graph of 5f(x) grows faster than the graph of f(x)

The graph of f(x) + 5 is shifted 5 units up from the graph of f(x).

Step-by-step explanation:

If the function g(x) = f(x) + c, we can say that g(x) is f(x) shifted c units up and if the function g(x) =cf(x), with c greater than 1, we can say that g(x) is a vertical stretch of f(x) by a factor of c.

Therefore, the graph of 5f(x) grows faster than the graph of f(x) because it is a vertical stretch of f(x) by a factor of 5, and the graph of f(x) + 5 is f(x) shifted 5 units up.

So, the answers are:

The graph of 5f(x) grows faster than the graph of f(x)

The graph of f(x) + 5 is shifted 5 units up from the graph of f(x).