Question

Describe the transformation from the graph of f to the graph of h. Write an equation that represents h in terms of x. Look at image for example. Let’s do problem number 11f(x)=2(x-1)^2 + 1h(x) = f(x-5)

Answer 1

$\begin{gathered} h(x)=2(x-6)^{2}+1 \\ So\:h\left(x\right)is\:horizontally\:translated\:5\:units\:to\:the\:right \end{gathered}$

1) Note that we can see the following function:

$f(x)=2\left(x-1\right)^2+1$

Note that we can see that this function f is vertically stretched, translated 1 unit to the side, and vertically shifted one unit

2) Now, let's visualize h(x):

$\begin{gathered} h(x)=f(x-5)=2((x-5)-1))^2+1 \\ h(x)=2\left(x-6\right)^2+1 \end{gathered}$

Note that the difference between the graph of f and the graph of h(x) is h(x) is translated 5 units to the right.

So h(x) is horizontally translated 5 units to the right