College Algebra, Chapter 3, 3.5, Section 3.5, Problem 52

Below is the graph of $f$. Match each equation with its graph.

"Please refer to the graph in the book"

a.) $\displaystyle y = \frac{1}{3} f(x)$

The graph of $\displaystyle y = \frac{1}{3} f(x)$ is obtained by shrinking the graph of $f(x)$ vertically by a factor of $\displaystyle \frac{1}{3}$. Thus, $\displaystyle y = \frac{1}{3} f(x)$ matches the graph number 2.

b.) $y = - f(x + 4)$

The graph of $y = - f(x + 4)$ is obtained by shifting the graph of $f(x)$ four units to the left and then the result is reflected about $x$-axis. Thus, $y = - f(x + 4)$ matches the graph number 3.

c.) $y = f(x - 4) + 3$

The graph of $y =f(x - 4) + 3$ is obtained by shifting the graph of $f(x)$ four units to the right and then the result is shifted 3 units upward. Thus, $y = f(x - 4) + 3$ matches the graph number 1.

d.) $y = f(-x)$

The graph of $y = f(-x)$ is obtained by reflecting the graph of $f(x)$ about $y$-axis. Thus, $y = f(-x)$ matches the graph number 4.