Questions: Functions and Their Graphs Online College Algebra 9101 Andrea Black 01/16/25 8:19 PM Functions and Question 13, 2.1.77 HW Score: 70.59%, 12 of 17 Part 2 of 6 Points: 0 of 1 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; and e. the missing function values, indicated by question marks, below. f(-2)=? f(2)=? a. The domain is (-∞, ∞). (Use interval notation.) b. The range is (Use interval notation.)

Functions and Their Graphs

Online College Algebra 9101 Andrea Black 01/16/25 8:19 PM Functions and Question 13, 2.1.77 HW Score: 70.59%, 12 of 17 Part 2 of 6 Points: 0 of 1

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; and e. the missing function values, indicated by question marks, below. f(-2)=? f(2)=? a. The domain is (-∞, ∞). (Use interval notation.) b. The range is (Use interval notation.)

Transcript text: Functions and Their Graphs Online College Algebra 9101 Andrea Black 01/16/25 8:19 PM Functions and Question 13, 2.1.77 HW Score: $70.59 \%$, 12 of 17 Part 2 of 6 Points: 0 of 1 Use the graph to determine $\mathbf{a}$. the function's domain; $\mathbf{b}$. the function's range; $\mathbf{c}$. the $x$-intercepts, if any; $\mathbf{d}$. the $y$-intercept, if any; and $e$. the missing function values, indicated by question marks, below. \[ f(-2)=? \quad f(2)=? \] a. The domain is $(-\infty, \infty)$. (Use interval notation.) b. The range is $\square$ (Use interval notation.)

Solution

Solution Steps

Step 1: Determine the domain

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this graph, the function extends infinitely in both the negative and positive x-directions, as indicated by the arrows. Therefore, the domain is all real numbers.

Step 2: Determine the range

The range of a function is the set of all possible output values (y-values). The lowest point on the graph is at $y=-1$, and the graph extends upwards infinitely. Therefore, the range is $[-1, \infty)$.

Step 3: Determine the x-intercepts

The x-intercepts are the points where the graph intersects the x-axis (i.e., where $y=0$). The graph intersects the x-axis at $x=1$ and $x=3$.

Step 4: Determine the y-intercept

The y-intercept is the point where the graph intersects the y-axis (i.e., where $x=0$). The graph intersects the y-axis at $y=3$.

Step 5: Determine f(-2)

$f(-2)$ is the y-value when $x=-2$. From the graph, when $x=-2$, $y=3$. Thus, $f(-2) = 3$.

Step 6: Determine f(2)

$f(2)$ is the y-value when $x=2$. From the graph, when $x=2$, $y=-1$. Thus, $f(2) = -1$.

Final Answer

a. The domain is $\boxed{(-\infty, \infty)}$. b. The range is $\boxed{[-1, \infty)}$. c. The x-intercepts are $\boxed{1 \text{ and } 3}$. d. The y-intercept is $\boxed{3}$. e. $f(-2) = \boxed{3}$ and $f(2) = \boxed{-1}$.

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