Question

Consider the graph of an absolute value function. How many y-intercepts can an absolute value function have?(1 point)
Responses

An absolute value function’s graph can have only 1 y-intercept.
An absolute value function’s graph can have only 1 y -intercept.

An absolute value function’s graph can have 0, 1, or 2 y-intercepts.
An absolute value function’s graph can have 0, 1, or 2 y -intercepts.

An absolute value function’s graph can have only 1 or 2 y-intercepts.
An absolute value function’s graph can have only 1 or 2 y -intercepts.

An absolute value function’s graph can have only 0 or 1 y-intercept.
An absolute value function’s graph can have only 0 or 1 y -intercept.

Answers

GPT-4o mini
An absolute value function has the general form \( f(x) = a |x - h| + k \), where \( (h, k) \) is the vertex of the graph. The graph of an absolute value function is a V-shaped curve that opens either upward or downward.

When considering y-intercepts, we find them by evaluating the function at \( x = 0 \). Thus, the y-intercept is at \( f(0) \). Because the function is continuous and defined for all real numbers, there will be one output (y-value) for the input \( x = 0 \).

Therefore, an absolute value function can have only **1 y-intercept**.

The correct response is:

**An absolute value function’s graph can have only 1 y-intercept.**

Related Questions