Question

(a) state the values of the following.
$g(3) = $
$g(1) = $
$g(4) = $
$g(2) = $
(b) for what value(s) of $x$ is $g(x) = 3$? (enter your answers as a comma - separated list.)

(c) for what value(s) of $x$ is $g(x) \leq 3$? (enter your answer using interval notation.)

(d) state the domain and range of $g$. (enter your answers using interval notation.)
domain
range
(e) on what interval(s) is $g$ increasing? (enter your answer using interval notation.)

Explanation:

Step1: Read g(3) from graph

Locate $x=3$ on the graph, the corresponding $y$-value is $1$.

Step2: Read g(1) from graph

Locate $x=1$ on the graph, the corresponding $y$-value is $1$.

Step3: Read g(4) from graph

Locate $x=4$ on the graph, the corresponding $y$-value is $0$.

Step4: Read g(2) from graph

Locate $x=2$ on the graph, the corresponding $y$-value is $3$.

Step5: Find x where g(x)=3

Identify points on the graph with $y=3$, their $x$-values are $-4, 2$.

Step6: Find x where g(x)≤3

Identify all $x$-values where the graph is at or below $y=3$: $[-4,4]$.

Step7: Find domain of g

Domain is all valid $x$-values from the graph: $[-4,4]$.

Step8: Find range of g

Range is all valid $y$-values from the graph: $[-2,3]$.

Step9: Find interval where g increases

Identify the $x$-interval where the graph rises: $[0,2]$.

Answer:

(a)
$g(3) = 1$
$g(1) = 1$
$g(4) = 0$
$g(2) = 3$

(b)
$-4, 2$

(c)
$[-4, 4]$

(d)
domain: $[-4, 4]$
range: $[-2, 3]$

(e)
$[0, 2]$