Questions: Use the graph of the function y=f(x) below to answer the questions. (a) Is f(-5) positive? Yes No (b) For which value(s) of x is f(x) ≥ 0 ? Write your answer using interval notation. (c) For which value(s) of x is f(x)=0 ? If there is more than one value, separate them with commas.

Use the graph of the function y=f(x) below to answer the questions.
(a) Is f(-5) positive?
Yes No
(b) For which value(s) of x is f(x) ≥ 0 ? Write your answer using interval notation.

(c) For which value(s) of x is f(x)=0 ?

If there is more than one value, separate them with commas.

Transcript text: Use the graph of the function $y=f(x)$ below to answer the questions. (a) Is $f(-5)$ positive? Yes No (b) For which value(s) of $x$ is $f(x) \geq 0$ ? Write your answer using interval notation. $\square$ (c) For which value(s) of $x$ is $f(x)=0$ ? If there is more than one value, separate them with commas. $\square$

Solution

Solution Steps

Step 1: Determine if f(-5) is positive

Looking at the graph, when x = -5, y = 3. Since 3 > 0, f(-5) is positive.

Step 2: Determine the interval(s) where f(x) ≥ 0

f(x) ≥ 0 when y ≥ 0 on the graph. This occurs where the graph is on or above the x-axis. Looking at the graph, this occurs when x is in the intervals [-5, -4] and [0, 3]. In interval notation: [-5, -4] ∪ [0, 3].

Step 3: Determine when f(x) = 0

f(x) = 0 represents the x-intercepts, where the graph crosses the x-axis. Examining the graph, this occurs at x = -4, x = 0, and x = 3.