Question

use the graph to determine a. the functions domain, b. the functions range, c. the x-intercepts, if any, d. the y-intercept, if any, and e. the missing function values, indicated by question marks, below

$a(-2)=7$ $a(7)=7$

a. the domain is $(-\infty, \infty)$ (type your answer in interval notation. simplify your answer)

Explanation:

Step1: Determine the domain

The domain of a function is the set of all possible \(x\)-values. Looking at the graph, there are no restrictions on the \(x\)-values. In interval notation, this is \((-\infty,\infty)\)

Step2: Determine the range

The range of a function is the set of all possible \(y\)-values. From the graph, the \(y\)-values start from \(-\infty\) (the graph goes downwards indefinitely) and has no upper - bound. So the range is \((-\infty,\infty)\)

Step3: Determine the \(x\)-intercepts

The \(x\)-intercepts are the points where \(y = 0\). From the graph, the function crosses the \(x\)-axis at \(x=-3\) and \(x = 3\). So the \(x\)-intercepts are \(-3\) and \(3\)

Step4: Determine the \(y\)-intercept

The \(y\)-intercept is the point where \(x = 0\). From the graph, when \(x = 0\), \(y=-9\). So the \(y\)-intercept is \(-9\)

Answer:

a. The domain is \((-\infty,\infty)\)
b. The range is \((-\infty,\infty)\)
c. The \(x\)-intercepts are \(-3\) and \(3\)
d. The \(y\)-intercept is \(-9\)