Chapter 1, Problem 4RE

Solution

To match the function represented in the graph with its equation.

The option $\text{h}$ , $f\left(x\right)=-\sin \left(x\right)$ , seems to be the best match of the function represented in the graph.

Given the graph of a function:

  

Concepts Used:

The sine function:

The sine function $f\left(x\right)=\sin \left(x\right)$ has the graph given below.

  

Reflection about the $x$-axis:

Given a function $y=f\left(x\right)$ .

The transformation $y=-f\left(x\right)$ reflects $y=f\left(x\right)$ about the $x$ -axis.

Determining the function:

Observe the graph of the function, it seems like a sine function reflected about the $x$ -axis.

Now, the sine function $f\left(x\right)=\sin \left(x\right)$ is reflected about the $x$ -axis when it is applied with the transformation $f\left(x\right)=-\sin \left(x\right)$ .

Thus, the function represented by the graph is $f\left(x\right)=-\sin \left(x\right)$ .

That is, the option $\text{h}$ represents the graph given in the problem.

Conclusion:

The option $\text{h}$ , $f\left(x\right)=-\sin \left(x\right)$ , seems to be the best match of the function represented in the graph.