Chapter 1.3, Problem 4E

(a)

To determine

To sketch: The graph of the function $y=f\left(x\right)-3$ by using the given graph.

Explanation of Solution

The equation $y=f\left(x\right)-3$ represents that the graph of the function is shifted 3 units downward. Thus, the graph of $y=f\left(x-4\right)$ is shown below in Figure 1.

From Figure 1, it is observed that the actual curve is shifted 3 units downward.

(b)

To determine

To sketch: The graph of the function $y=f\left(x+1\right)$ by using the given graph.

Explanation of Solution

The equation $y=f\left(x\right)+1$ represents that the graph of the function is shifted 1 unit to the left side. Thus, the graph of $y=f\left(x+1\right)$ is shown below.

From Figure 2, it is observed that the actual curve is shifted 1 unit to the left.

(c)

To determine

To sketch: The graph of the function $y=\frac{1}{2}f\left(x\right)$ by using the given graph.

Explanation of Solution

The equation $y=\frac{1}{2}f\left(x\right)$ represents that the graph of the function is shrunk vertically by a factor of 2. Thus, the graph of $y=\frac{1}{2}f\left(x\right)$ is shown below in Figure 3.

From Figure 3, it is observed that the actual curve is shrunk vertically 2 units by a factor of 2.

(d)

To determine

To sketch: The graph of the function $y=-f\left(x\right)$ by using the given graph.

Explanation of Solution

The equation $y=-f\left(x\right)$ represents that the graph of the function is reflected about the x-axis. Thus, the graph of $y=-f\left(x\right)$ is shown below in Figure 4.

From Figure 4, it is observed that the actual curve is reflected about the origin.