-- - 15, I< -5 f(x) = { Ma + B, 2+7, - 5 < * < 3 x > 3 The values of M and B that make f(æ) continuous are: 1. M = 2. B = In your written work, justify why f(z) is continuous with your chosen values of M and B. Be sure to use one-sided limits and the definition of continuity in your justification.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
### Continuity Problem

Determine the values of \( M \) and \( B \) that make the function \( f(x) \) continuous:

\[ 
f(x) = 
\begin{cases} 
-\frac{2}{5}x - 15, & x \leq -5 \\
Mx + B, & -5 < x \leq 3 \\
4x + 7, & x > 3
\end{cases} 
\]

**Values to Determine:**

1. \( M = \) [Input Required]
2. \( B = \) [Input Required]

**Instruction:**

In your written work, justify why \( f(x) \) is continuous with your chosen values of \( M \) and \( B \). Be sure to use one-sided limits and the definition of continuity in your justification.
Transcribed Image Text:### Continuity Problem Determine the values of \( M \) and \( B \) that make the function \( f(x) \) continuous: \[ f(x) = \begin{cases} -\frac{2}{5}x - 15, & x \leq -5 \\ Mx + B, & -5 < x \leq 3 \\ 4x + 7, & x > 3 \end{cases} \] **Values to Determine:** 1. \( M = \) [Input Required] 2. \( B = \) [Input Required] **Instruction:** In your written work, justify why \( f(x) \) is continuous with your chosen values of \( M \) and \( B \). Be sure to use one-sided limits and the definition of continuity in your justification.
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