Chapter 3.8, Problem 28PPS

To determine

To determine the domain and range of the function from the given graph.

Answer to Problem 28PPS

Domain: $x\in ℝ$

Range: $y\in \left[-3,\infty \right)$

Explanation of Solution

Given:

  

Concept used:

The general form of an absolute value function is $f(x)=a\left|x-h\right|+k$ .

Calculation:

Let the function be $f(x)$ .

From the graph, the vertex of the function is at $\left(1,-3\right)$ .

Interpretation:

From the graph, it can be observed that the horizontal extent of the graph is from $-\infty$ to $\infty$ , so the domain of $g(x)$ is $\left(-\infty ,\infty \right)$ .

The vertical extent of the graph is from $-3$ to $\infty$ , so the range of $g(x)$ is $\left[-3,\infty \right)$ .

Conclusion:

Therefore, the domain of $f(x)$ is $x\in ℝ$ and range is $y\in \left[-3,\infty \right)$ .