Question

use the graph to determine a. the function’s domain, b. the function’s range, c. the x - intercepts, if any, d. the y - intercept, if any, e. the function values. (5 - 4) what is the domain? (type your answer in interval notation)

Explanation:

Step1: Identify domain (x-values)

The graph has closed endpoints at $x=-4$ and $x=6$, so all x-values between these are included.
Domain: $[-4, 6]$

Step2: Identify range (y-values)

The graph has closed endpoints at $y=0$ and $y=4$, so all y-values between these are included.
Range: $[0, 4]$

Step3: Find x-intercept

The graph crosses the x-axis at $x=6$, where $y=0$.
x-intercept: $(6, 0)$

Step4: Find y-intercept

The graph crosses the y-axis at $y=3$, where $x=0$.
y-intercept: $(0, 3)$

Step5: Calculate $f(-4)$

At $x=-4$, the graph has $y=4$.
$f(-4)=4$

Answer:

a. Domain: $[-4, 6]$
b. Range: $[0, 4]$
c. x-intercept: $(6, 0)$
d. y-intercept: $(0, 3)$
e. $f(-4)=4$