Math Problem Statement

p(x)={(-3x-2 x<=2),(4x^(2)+2x-7 x>2):}find p(-6)

Solution

The piecewise function is defined as:

\begin{cases} -3x - 2 & \text{if } x \leq 2 \\ 4x^2 + 2x - 7 & \text{if } x > 2 \end{cases}$$ To find $$p(-6)$$, we first determine which part of the piecewise function to use. Since $$-6 \leq 2$$, we will use the first part of the function, which is $$p(x) = -3x - 2$$. Now substitute $$x = -6$$ into this equation: $$p(-6) = -3(-6) - 2 = 18 - 2 = 16$$ So, $$p(-6) = 16$$. Would you like more details, or do you have any questions? Here are 5 related questions to expand on this: 1. How would you find $$p(0)$$? 2. What is $$p(3)$$ using the piecewise function? 3. How do you determine which part of a piecewise function to use? 4. What is the domain of this piecewise function? 5. Can you find where the two parts of the function meet at $$x = 2$$? **Tip:** When working with piecewise functions, always check which condition your input satisfies before substituting into the appropriate expression.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Linear Equations
Quadratic Functions

Formulas

p(x) = -3x - 2 (if x <= 2)
p(x) = 4x^2 + 2x - 7 (if x > 2)

Theorems

Piecewise function definition

Suitable Grade Level

Grades 9-11