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

1 answer

To determine how many y-intercepts an absolute value function can have, let's consider the general format of an absolute value function, which is typically expressed as \( y = a |x - h| + k \), where \( a \), \( h \), and \( k \) are constants.

The y-intercept occurs when \( x = 0 \). To find the y-intercept of the function, you simply evaluate \( y \) when \( x = 0 \):

\[ y = a |0 - h| + k = a |h| + k \]

This will always yield a value for \( y \) regardless of the values of \( a \), \( h \), and \( k \). Thus, for any absolute value function, there will always be exactly one y-intercept.

Therefore, the correct response is:

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