Question

g(x) = f(x) + 11

select the correct choice below, and fill in the answer box to complete your choice

a. g(x) has a scale factor of \\(\square\\) compared to f(x). because it scales the vertical direction, the graph is stretched vertically
b. g(x) has a scale factor of \\(\square\\) compared to f(x). because it scales the horizontal direction, the graph is stretched horizontally
c. g(x) has a scale factor of \\(\square\\) compared to f(x). because it scales the horizontal direction, the graph is compressed horizontally
d. the graph of g(x) is translated \\(\square\\) unit(s) down compared to graph of f(x)
e. the graph of g(x) is translated \\(\square\\) unit(s) to the left compared to the graph of f(x)
f. the graph of g(x) is translated \\(\square\\) unit(s) to the right compared to the graph of f(x)
g. g(x) has a scale factor of \\(\square\\) compared to f(x). because it scales the vertical direction, the graph is compressed vertically
h. the graph of g(x) is translated \\(\square\\) unit(s) up compared to graph of f(x)

Explanation:

Step1: Identify transformation type

The function is \(g(x) = f(x) + 11\), which is a vertical translation (no scaling, as there’s no coefficient multiplying \(f(x)\)).

Step2: Determine translation direction/magnitude

Adding a positive constant to \(f(x)\) translates the graph upward by that constant’s value.

Answer:

H. The graph of g(x) is translated 11 unit(s) up compared to graph of f(x)