Question

In the piecewise function below, what does y equal when x = -2?

x + 3 & \text{if } x < -1 \\
x^2 & \text{if } x \geq -1
\end{cases}]
a) 1
b) 5
c) 4
d) 9

Answer 1

When x = -2, the value of y in the piecewise function is 1.

Step-by-step explanation:

To find the value of y when x = -2 in the given piecewise function, we must consider the conditions for each part of the function. For x < -1, the expression is x + 3, and for x ≥ -1, the expression is x². Since x = -2 falls into the first condition (x < -1), we substitute -2 into the expression x + 3: y = -2 + 3 = 1. Therefore, when x = -2, y equals 1 according to the piecewise function.

Understanding piecewise functions involves recognizing the different expressions that apply to specific ranges of x-values. In this case, when x is less than -1, the function is linear (x + 3), and for x greater than or equal to -1, it becomes quadratic (x²). Evaluating the function at x = -2, we follow the appropriate expression based on the conditions, leading to the result y = 1.

In summary, by adhering to the conditions specified in the piecewise function and substituting x = -2 into the corresponding expression, we find that y equals 1. This showcases the versatility of piecewise functions in handling different mathematical expressions for distinct intervals of the independent variable.