Question

Consider the functions f(x) = (x - 5)^2 + 2 and g(x) = (x + 6)^2 - 4. Which of the following statements is true?

Answer 1

To solve the question, we can plot the two functions on the same graph as shown below

The blue graph is that for the function g(x)

While that of the red graph is that of the function f(x)

We can observe that the graph of g(x) is

$\begin{gathered} 2-(-4)=6 \\ 6\text{units below f(x)} \end{gathered}$

Also,

$g(x)\text{ is 11 units to left of f(x)}$

Thus, we can see that

The graph of g(x) is shifted 6 units below and 11 units to the left of the graph f(x)

Thus, option C is correct