Math Problem Statement
Given the following piecewise function, evaluate
f
(
−
6
)
.
f
(
x
)
{ − 5 x + 7 x < − 6 6 x − 3 x ≥ − 6
Solution
To evaluate for the given piecewise function, we need to determine which piece of the function applies when .
The given piecewise function is:
\begin{cases} -5x + 7 & \text{if } x < -6 \\ 6x - 3 & \text{if } x \geq -6 \end{cases}$$ Since $$x = -6$$ falls under the condition $$x \geq -6$$, we will use the second piece of the function, which is $$6x - 3$$. Now, substitute $$x = -6$$ into this equation: $$f(-6) = 6(-6) - 3$$ $$f(-6) = -36 - 3$$ $$f(-6) = -39$$ Thus, $$f(-6) = -39$$. Would you like a further explanation of piecewise functions or any other details? Here are some related questions: 1. What is the difference between a piecewise function and a continuous function? 2. How would you graph a piecewise function? 3. Can piecewise functions have more than two conditions? 4. How do you evaluate limits of piecewise functions at boundary points? 5. What happens if $$x$$ is exactly at the boundary between two conditions in a piecewise function? **Tip:** When evaluating piecewise functions, always check which condition the input value satisfies before applying the corresponding formula!Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Inequalities
Formulas
f(x) = -5x + 7 (for x < -6)
f(x) = 6x - 3 (for x ≥ -6)
Theorems
Piecewise function evaluation
Suitable Grade Level
Grades 9-11