Question

question 18 of 42
what is the range for the graph below?
a. all real numbers
b. all real numbers except -3
c. all real numbers except 0
d. all real numbers except -3 and 0

Explanation:

Step1: Recall Range Definition

Range is the set of all possible y - values of a function.

Step2: Analyze the Graph

The graph appears to be a hyperbola (likely a rational function). Looking at the y - axis, we can see that the graph never reaches \(y=- 3\). The horizontal asymptote seems to be \(y = - 3\), meaning the function's output (y - values) can be any real number except \(-3\). Let's check the options:

• Option A: All real numbers is incorrect because \(y=-3\) is not achieved.
• Option B: All real numbers except \(-3\) matches our analysis.
• Option C: The graph does not have a restriction around \(y = 0\) in terms of range (the graph can take values around 0), so this is incorrect.
• Option D: There is no restriction around \(y = 0\) for the range, so this is incorrect.

Answer:

B. All real numbers except -3