Question

use the graph to determine a. the functions domain; b. the functions range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function value, indicated by the question mark below.
\\( f(16) = ? \\)

a. the domain of the function is \\(\square\\). (type your answer in interval notation.)

Explanation:

Step1: Identify domain from graph

The graph starts at $x=0$ (closed dot) and ends at $x=20$ (closed dot), so all $x$-values between and including these points are valid.
Domain: $[0, 20]$

Step2: Identify range from graph

The lowest $y$-value is $2$ (at $x=0$) and the highest is $6$ (at $x=20$), with all values in between covered.
Range: $[2, 6]$

Step3: Find x-intercepts

An x-intercept is where $y=0$. The graph never touches $y=0$, so there are no x-intercepts.

Step4: Find y-intercept

The y-intercept is where $x=0$. At $x=0$, $y=2$.
Y-intercept: $(0, 2)$

Step5: Find $t(16)$

Locate $x=16$ on the graph, the corresponding $y$-value is $6$.
$t(16)=6$

Answer:

a. $[0, 20]$
b. $[2, 6]$
c. No x-intercepts
d. $(0, 2)$
e. $6$