Chapter 1, Problem 1RE

Solution

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

The option $\text{d}$ , $f\left(x\right)={\left(x+2\right)}^2$ , seems to be the best match of the function represented in the graph.

Given the graph of a function:

  

Determining the function:

Observing the graph of the function form the left side, it touches $x=-2$ and rises back to the same side of incidence. Also, the function seems to have no other zeroes.

Thus, $x=-2$ is the only zero of the function and it has some even degree.

Among the options, $f\left(x\right)={\left(x+2\right)}^2$ is the only one satisfying both the findings that $x=-2$ is the only zero of the function and it has some even degree.

Conclusion:

The option $\text{d}$ , $f\left(x\right)={\left(x+2\right)}^2$ , seems to be the best match of the function represented in the graph.