Questions: x -3 -1 2 6 9
p(x) f(6) e -1 1 3
h(x) =
8(1/2)^x, for x<2
1-x^2, for x=2
4, for x>3
The function m is the result of applying three transformations to the graph of g in this order: a vertical dilation by a factor of 2, a vertical translation by -3 units, and a horizontal translation by 1 unit. m(x) = 2(g(x-1)) - 3
Directions: Use the given information above to evaluate the following, if possible.
18. (g ∘ g)(-2)
Transcript text: \begin{tabular}{|c|c|c|c|c|c|}
\hline$x$ & -3 & -1 & 2 & 6 & 9 \\
\hline$p(x)$ & $f(6)$ & $e$ & -1 & 1 & 3 \\
\hline
\end{tabular}
\[
h(x)=\left\{\begin{array}{cc}
8\left(\frac{1}{2}\right)^{x}, & x<2 \\
1-x^{2}, & x=2 \\
4, & x>3
\end{array}\right.
\]
The function $m$ is is the result of applying three transformations to the graph of $g$ in this order: a vertical dilation by a factor of 2 , a vertical translation by -3 units, and a horizontal translation by 1 unit. $m(x)=2(g(x-1))-3$
Directions: Usethe givenimformation above to evaluate the following, if possible.
18. $(g \circ g)(-2)$
Solution
Solution Steps
Step 1: Find g(-2)
From the graph of g(x), we can observe that when x = -2, g(-2) = 3.
Step 2: Evaluate (g ° g)(-2)
(g ° g)(-2) means g(g(-2)). Since g(-2) = 3, we need to find g(3). Looking at the graph of g(x), when x = 3, g(3) = 2.