Question

use the graph of the function f shown to answer parts (a)-(n).
the domain of f is {x| - 21≤x≤21} (type a compound - inequality.)
what is the domain of f? (g)

• 21<x< - 5,13<x<21 (type a compound inequality. use a comma to separate answers as needed.)

for what values of x is f(x)>0? (i)
x = - 21, - 5,13 (use a comma to separate answers as needed.)
what is the range of f? (h)
the range of f is {y|}

Explanation:

Step1: Identify domain from graph

The domain is the set of all x - values for which the function is defined. Looking at the graph, the x - values range from - 21 to 21. So the domain in compound - inequality form is $-21\leq x\leq21$.

Step2: Identify range from graph

The range is the set of all y - values that the function takes. By observing the y - coordinates of the points on the graph, the lowest y - value is - 2 and the highest is 3. So the range is $\{y|-2\leq y\leq3\}$.

Step3: Find x for f(x)>0

We look at the parts of the graph where the y - values (f(x)) are above the x - axis (y = 0). From the graph, we can see that $f(x)>0$ when $-21 < x < - 18$ or $-6 < x < 9$.

Answer:

(g) The domain of $f$ is $\{x|-21\leq x\leq21\}$ (already given correctly in the problem).
(h) The range of $f$ is $\{y|-2\leq y\leq3\}$.
(i) For what values of $x$ is $f(x)>0$? The answer is $-21 < x < - 18,-6 < x < 9$.