Evaluating Piecewise Functions: Example with f(x) for x = -3, 0, and 3

Math Problem Statement

Evaluate the piecewise function at the given values of the independent variable.

f left parenthesis x right parenthesis equals left brace Start 2 By 2 Matrix 1st Row 1st Column 5 x plus 5 2nd Column if x less than 0 2nd Row 1st Column 3 x plus 7 2nd Column if x greater than or equals 0 EndMatrixf(x)=

5x+5

if x<0

3x+7

if x≥0

(a) f left parenthesis negative 3 right parenthesisf(−3)

(b) f left parenthesis 0 right parenthesisf(0)

Question content area bottom

Part 1

(a)

f left parenthesis negative 3 right parenthesisf(−3)equals=enter your response here

Part 2

(b)

f left parenthesis 0 right parenthesisf(0)equals=enter your response here

Part 3

(c)

f left parenthesis 3 right parenthesisf(3)equals=enter your response here

Solution

We are given a piecewise function:

5x + 5 & \text{if } x < 0 \\ 3x + 7 & \text{if } x \geq 0 \end{cases}$$ Now, let's evaluate the function at each of the given values. ### Part 1: $$f(-3)$$ Since $$-3 < 0$$, we will use the first part of the piecewise function: $$f(-3) = 5(-3) + 5 = -15 + 5 = -10$$ Thus, $$f(-3) = -10$$. ### Part 2: $$f(0)$$ Since $$0 \geq 0$$, we will use the second part of the piecewise function: $$f(0) = 3(0) + 7 = 0 + 7 = 7$$ Thus, $$f(0) = 7$$. ### Part 3: $$f(3)$$ Since $$3 \geq 0$$, we will again use the second part of the piecewise function: $$f(3) = 3(3) + 7 = 9 + 7 = 16$$ Thus, $$f(3) = 16$$. ### Final answers: (a) $$f(-3) = -10$$ (b) $$f(0) = 7$$ (c) $$f(3) = 16$$ --- Do you need more details or have any questions? Here are five follow-up questions: 1. What is the general definition of a piecewise function? 2. How do you determine which part of the piecewise function to use? 3. How would the function change if the condition for $$x \geq 0$$ was modified to $$x > 0$$? 4. What would $$f(1)$$ be in this piecewise function? 5. Can you graph this piecewise function and identify any points of discontinuity? **Tip:** Always check the conditions carefully to decide which piece of the function applies when working with piecewise functions!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Algebra
Function Evaluation

Formulas

f(x) = { 5x + 5, if x < 0; 3x + 7, if x ≥ 0 }

Theorems

Suitable Grade Level

Grades 8-10

Related Recommendation

Evaluating a Piecewise Function for f(x) at x = -1, 0, and 4

Evaluate a Piecewise Function at Specific Points

Evaluating Piecewise Function f(x) = 4 if x ≤ 3, 3x - 5 if x > 3

Evaluate Piecewise Function f(x) = { x if x < 0, 5x + 8 if x >= 0 }

Piecewise Function Evaluation and Graphing: Solve for f(3), f(5), and f(7)