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?

(h) the function has no smallest value over any open interval so there is no relative minimum.
the relative maximum of the graph is where f(x) =

(i) f(x) = 3 where x = (use a comma to separate answers as needed.)

(j) is f(-2) positive or negative?
positive

Explanation:

Find the relative maximum

Using the Function Behavior from Graph knowledge point

$$ \text{The peak of the curve occurs at the point } (-3, 3). $$

$$ \text{Therefore, the relative maximum of the graph is where } f(x) = 3. $$

Find the x-values where f(x) = 3

Using the Function Behavior from Graph knowledge point

$$ \text{The horizontal line } y = 3 \text{ intersects the graph at the vertex } (-3, 3). $$

$$ \text{Thus, } f(x) = 3 \text{ where } x = -3. $$

Determine if f(-2) is positive or negative

Using the Function Behavior from Graph knowledge point

$$ \text{At } x = -2, \text{ the corresponding point on the graph is } (-2, 2). $$

$$ \text{Since the } y\text{-value is } 2 > 0, \text{ the value of } f(-2) \text{ is positive.} $$

Answer:

Question (h)

The relative maximum of the graph is where \(f(x) =\) <blank>3</blank>

Question (i)

\(f(x) = 3\) where \(x =\) <blank>-3</blank>

Question (j)

Is \(f(-2)\) positive or negative?

• Positive (Correct answer)
• Negative