Select the correct answer.

What is the $y$-intercept of function $f$ ?

$f(x)=\left\{\begin{array}{ll}
-3 x-2, & -\infty
-x+1, & -2 \leq x<3 \\
2 x+5, & 3 \leq x<\infty
\end{array}\right.$

A. 5
B. -2
C. -1
D. 1

To find the y -intercept, set x = 0 .
Determine which piece of the piecewise function applies when x = 0 .
Since − 2 ≤ 0 < 3 , use the function f ( x ) = − x + 1 .
Evaluate f ( 0 ) = − 0 + 1 = 1 , so the y -intercept is 1 ​ .

Explanation

Finding the y-intercept To find the y -intercept of the function f ( x ) , we need to find the value of f ( x ) when x = 0 . The function f ( x ) is defined piecewise, so we need to determine which piece of the function applies when x = 0 .

Identifying the correct interval The function is defined as:


$f(x)=\left{\begin{array}{ll} -3 x-2, & -\infty

Answered by GinnyAnswer | 2025-07-05