Chapter 1.3, Problem 6E

Solution

To match: the given graph with its function and verify with graphing window $\left[-4.7,4.7\right]\times \left[-3.1\times 3.1\right]$ .

The given graph matches with option (f) $y={\left(x-1\right)}^2$ .

Given information: The given graph is,

  

Formula used:

The graph of the function $y=f\left(x-h\right)$ is found by shifting the graph of the function $y=f\left(x\right)$ by $h$ units right.

Calculation:

See the shape of the graph.

The graph resembles to the graph of $y=x^2$ .

Consider the basic function $y=x^2$ .

Shift the graph 1 unit to right such that the $x$ -intercept is $-1$ .

Thus, the graph of the function is $y={\left(x-1\right)}^2$

The given graph matches with option (f).

Graph the function in the graphing window $\left[-4.7,4.7\right]\times \left[-3.1\times 3.1\right]$, by using graphing calculator:

  

Hence, the graph matches with option (f) $y={\left(x-1\right)}^2$ .