Question

use the graph of the function f shown to answer parts (a)-(n). (g) what is the domain of f? 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| -2≤y≤3} (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 = -1 (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? time(s)

Explanation:

Step1: Analyze domain from graph

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 from graph

The range is the set of all y - values that the function takes. The lowest y - value is $y=-2$ and the highest is $y = 3$. So, the range is $-2\leq y\leq3$.

Step3: Find x - intercepts

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

Step4: Find y - intercepts

The y - intercept is the y - value where the graph crosses the y - axis (where $x = 0$). From the graph, this occurs at $y=-1$.

Step5: Find intersections with $y = 1$

By looking at the graph, count the number of times the horizontal line $y = 1$ crosses the graph of the function. The line $y = 1$ intersects the graph 3 times.

Answer:

(g) $-21\leq x\leq18$
(h) $-2\leq y\leq3$
(i) $-18,-3,12$
(j) $-1$
(k) 3