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(-0.5)
(e) the intervals on which f is increasing
(f) the intervals on which f is decreasing
(g) the values for which f(x) \le 0
(h) any relative maxima or minima
(i) the value(s) of x for which f(x) = 3
(j) is f(-2) 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 -6 and the right zero is
(d) f(-0.5) =
(e) the interval on which f is increasing is (type your answer in interval notation.)
(f) the interval on which f is decreasing is (type your answer in interval notation.)

Explanation:

Find the domain and range

Using the Interval Notation knowledge point

$$
LATEXBLOCK0
$$

Find the zeros and evaluate the function

The graph intersects the \(x\)-axis at \(x = -6\) and \(x = -1\). Thus, the right zero is \(-1\).
To find \(f(-0.5)\), we locate \(x = -0.5\) on the graph and find the corresponding \(y\)-value, which is \(1\).

Determine intervals of increase and decrease

Using the Interval Notation knowledge point

$$
LATEXBLOCK1
$$

Answer:

Question 1

(a) The domain of \(f\) is <blank>\([-6, 0]\)</blank>

Question 2

(b) The range of \(f\) is <blank>\([-4, 3]\)</blank>

Question 3

(c) The left zero of the function is \(-6\) and the right zero is <blank>\(-1\)</blank>

Question 4

(d) \(f(-0.5) =\) <blank>\(1\)</blank>

Question 5

(e) The interval on which \(f\) is increasing is <blank>\([-6, -3]\)</blank>

Question 6

(f) The interval on which \(f\) is decreasing is <blank>\([-3, 0]\)</blank>