Question

use the graph of f to determine each of the following.
(a) the domain of f
(b) the range of f
(c) the zeros of f
(d) f(4)
(e) the intervals on which f is increasing
(f) the intervals on which f is decreasing
(g) the values for which f(x) ≤ 0
(h) any relative maxima or minima
(i) the value(s) of x for which f(x) = 4
(j) is f(3) positive or negative?
(a) the domain of f is □. (type your answer in interval notation.)
(b) the range of f is □ (type your answer in interval notation.)
(c) the left zero of the function is -2.5 and the right zero is □.
(d) f(4) = □
(e) the interval on which f is increasing is □. (type your answer in interval notation.)

Explanation:

Step1: Find the domain

The domain is all \(x -\)values covered by the graph. The graph extends from \(x=-5\) to \(x = 6\). So the domain is \([-5,6]\).

Step2: Find the range

The range is all \(y -\)values covered by the graph. The lowest \(y -\)value is \(-5\) and the highest \(y -\)value is \(4\). So the range is \([-5,4]\).

Step3: Find the right - zero

The zeros of the function are the \(x -\)values where \(y = f(x)=0\). We know one zero is \(x=-2.5\). Looking at the graph, the other zero is \(x = 5\).

Step4: Find \(f(4)\)

To find \(f(4)\), we look at the \(y -\)value when \(x = 4\). From the graph, when \(x = 4\), \(y=2\), so \(f(4)=2\).

Step5: Find the increasing interval

A function is increasing when as \(x\) increases, \(y\) increases. Looking at the graph, the function is increasing on the interval \([-5,1]\).

Answer:

(a) \([-5,6]\)
(b) \([-5,4]\)
(c) \(5\)
(d) \(2\)
(e) \([-5,1]\)