Math Problem Statement

For the indicated​ function, find the values

​f(negative 4−4​),

​f(00​),

and

​f(66​).

f left parenthesis x right parenthesis equals StartSet Start 2 By 1 Matrix 1st Row 1st Column x comma if x less than 0 2nd Row 1st Column 5 x plus 8 comma if x greater than or equals 0 EndMatrixf(x)=

       x, if x<0

5x+8, if x≥0

Question content area bottom

Part 1

​f(negative 4−4​)equals=enter your response here

Part 2

​f(00​)equals=enter your response here

Part 3

​f(66​)equals=enter your response here

Solution

Given the piecewise function:

\begin{cases} x & \text{if } x < 0 \\ 5x + 8 & \text{if } x \geq 0 \end{cases}$$ We need to find the values of $$f(-4)$$, $$f(0)$$, and $$f(6)$$. ### Part 1: Calculate $$f(-4)$$ Since $$-4 < 0$$, we use the first part of the function: $$f(-4) = -4$$ ### Part 2: Calculate $$f(0)$$ Since $$0 \geq 0$$, we use the second part of the function: $$f(0) = 5(0) + 8 = 0 + 8 = 8$$ ### Part 3: Calculate $$f(6)$$ Since $$6 \geq 0$$, we use the second part of the function: $$f(6) = 5(6) + 8 = 30 + 8 = 38$$ ### Final Answers $$f(-4) = -4$$ $$f(0) = 8$$ $$f(6) = 38$$ Would you like further details or have any questions? ### Relative Questions: 1. How do you graph a piecewise function like the one given? 2. What are the key steps to evaluating a piecewise function at a given value? 3. How do you determine where a piecewise function is continuous? 4. How would you define a piecewise function with more than two pieces? 5. What are the applications of piecewise functions in real-world scenarios? ### Tip: Always carefully check the conditions in a piecewise function before substituting values to ensure you're using the correct piece of the function.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-12

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