Question

2.3.3 quiz: graphs of functions
a. $-7 \leq y \leq 7$
b. $y = 1.5$
c. $x \leq 0$
d. $x$ is all real numbers.

Explanation:

Step1: Analyze the graph

The graph is a horizontal line, which represents a constant function. For a horizontal line, the \( y \)-value is constant, and the \( x \)-value can be any real number (since the line extends infinitely in both horizontal directions).

Step2: Evaluate each option

• Option A: The graph doesn't show \( y \) values between -7 and 7 (it's a horizontal line at a specific \( y \)-value, not a range like this), so A is incorrect.
• Option B: The graph appears to be at \( y = 1.5 \)? Wait, no, looking at the grid, the horizontal line is at \( y = 1 \)? Wait, maybe the grid lines: but regardless, the key is about the domain (x-values) or range (y-values). Wait, the question is probably about the domain or range. Wait, the options: A is range, B is a specific y, C is x ≤ 0 (domain), D is x is all real numbers (domain).

Wait, the graph is a horizontal line, so the domain (x-values) is all real numbers because the line goes left and right infinitely. The range would be a single y-value. Let's re-express:

For a horizontal line (constant function), the domain (set of x-values) is all real numbers (since x can be any real number, as the line extends horizontally without bound), and the range is a single y-value.

Now, let's check the options:

• A: \( -7 \leq y \leq 7 \): The range here is an interval, but a horizontal line has a single y-value, so A is wrong.
• B: \( y = 1.5 \): If the horizontal line is at \( y = 1.5 \) (or whatever the correct y-value is from the graph), but the question is about which option is correct. Wait, maybe the graph is \( y = 1 \) or \( y = 0 \)? Wait, the red line is horizontal, probably at \( y = 1 \) or maybe \( y = 0 \)? Wait, the grid: the x-axis is the horizontal line through the origin, but the red line is a horizontal line above or below? Wait, the graph shows a horizontal line, so the domain (x-values) is all real numbers (option D), or the range? Wait, the options:

A: range (y-values between -7 and 7)

B: specific y-value

C: x ≤ 0 (domain, x-values ≤ 0)

D: x is all real numbers (domain, x can be any real number)

Since the graph is a horizontal line, it extends infinitely in the x-direction (left and right), so the domain (x-values) is all real numbers. So D is correct.

Answer:

D. \( x \) is all real numbers.