Question

use the graph of the function f shown to answer parts (a)-(n). the domain of f is {x| - 21≤x≤18}. (type a compound inequality.) (h) what is the range of f? the range of f is {y| - 8≤y≤12}. (type a compound inequality.) (i) what are the x - intercept(s)? x = - 18, - 3,12 (type an integer or a simplified fraction. use a comma to separate answers as needed.) (j) what are the y - intercept(s)? y = - 4 (type an integer or a simplified fraction. use a comma to separate answers as needed.) (k) how often does the line y = 1 intersect the graph? 3 time(s) (l) how often does the line x = 1 intersect the graph? time(s)

Explanation:

Step1: Analyze domain

The domain is the set of all x - values for which the function is defined. Looking at the graph, the left - most x - value is $x=-21$ and the right - most is $x = 18$, so the domain is $-21\leq x\leq18$.

Step2: Analyze range

The range is the set of all y - values. The lowest y - value is $y=-8$ and the highest is $y = 12$, so the range is $-8\leq y\leq12$.

Step3: Find x - intercepts

The x - intercepts are the points where the graph crosses the x - axis ($y = 0$). From the graph, these occur at $x=-18,x=-3,x = 12$.

Step4: Find y - intercepts

The y - intercept is the point where the graph crosses the y - axis ($x = 0$). From the graph, it is at $y=-4$.

Step5: Analyze $y = 1$ intersection

Draw the line $y = 1$ on the graph. Count the number of times it intersects the graph of $y=f(x)$. It intersects 3 times.

Step6: Analyze $x = 1$ intersection

Draw the line $x = 1$ on the graph. Count the number of times it intersects the graph of $y=f(x)$. It intersects 1 time.

Answer:

(h) $\{y|-8\leq y\leq12\}$
(i) $x=-18,-3,12$
(j) $y=-4$
(k) 3
(l) 1