Question

translate each Graph as specified below(a)the graph of y=(x)+4 is shown. Translate it to get the graph of y=f(x)+4(b) The graph of y=g(x) is shown. Translate it to get the graph of y=g(x-2).

Answer 1

Solution:

Given the graphs (a) and (b)

a) The function of graph (a) is

$f(x)=-4\sqrt{x+3}+1$

The graph of the function is shown below

Translating it to get the graph of

$y=f(x)+4$

The translated function becomes

$\begin{gathered} y=f(x)+4 \\ y=(-4\sqrt{x+3}+1)+4 \\ y=-4\sqrt{x+3}+1+4 \\ y=-4\sqrt{x+3}+5 \end{gathered}$

The translated graph is

b) The function of graph (a) is

$g(x)=-|x|$

The graph of the function is shown below

Translating it to get the graph of

$y=g(x-2)$

The translated function becomes

$\begin{gathered} y=g(x-2) \\ y=-|x-2| \end{gathered}$

The translated graph is