Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 52

Estimate the value of $f(g(x))$ for $x = -5, -4, -3 ..... 5 $ by using the given graphs of $f$ and $g$ below. Sketch a rough graph of $f \circ g$ using the estimated value.




Referring to the graph given the estimated values of $x$ are

$
\begin{array}{|c|c|c|}
\hline\\
x & g(x) & (f \circ g )/ y\\
\hline\\
-5 & -0.2 & -3.9\\
-4 & 1.25 & -3.1\\
-3 & 2.25 & -1.7\\
-2 & 2.75 & -0.5\\
-1 & 3 & -0.1\\
0 & 2.75 & -0.5\\
1 & 2.25 & -1.7\\
2 & 1.25 & -3.1\\
3 & -0.2 & -3.9\\
4 & -2 & -2.1\\
5 & -4.25 & 2.25\\
\hline
\end{array}
$




By plotting the points, the graph will look like