+13 if z<8 V8 a +9 if r 2 8 Analyze the function f (x) = Your classmates may be analyzing different functions, so in your initial post in Brightspace be sure to specify the function that you are analyzing. Part 1: Is f (x) continuous at z = 8? Explain why or why not in your Discussion post

Calculus: Early Transcendentals
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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...
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Hi, so I just need help explaining why part 2 is yes. thank you. 

MAT-225-X4467 21EW4 Calc I: Single-Variable Calc
Module Three
3-1 Module Three Discussion: Continuity and Differentiability
3-1 Module Three Discussion: Continuity and Differentiability
Remaining Time: Unlimited
{
Module Three Discussion
x + 13
if x < 8
Analyze the function f (x) =
V8 x +9 if x> 8
Your classmates may be analyzing different functions, so in your initial post in Brightspace be sure to specify the function that you are analyzing.
Part 1: Is f (x) continuous at x = 8? Explain why or why not in your Discussion post
O Yes
O No
Hint: In order for f (x) to be continuous at x = 8, the limits of f (x) from the left and from the right must both exist and be equal to f (8).
Part 2: Is f(x) differentiable at x = 8? Explain why or why not in your Discussion post.
O Yes
O No
Hint: Similarly to continuity, in order for f (x) to be differentiable at x = 8, f (x) must be continuous at x =8 and the limits of the difference quotient
f(8+h)-f(8)
from the left and from the right must both exist and be equal to each other.
Transcribed Image Text:MAT-225-X4467 21EW4 Calc I: Single-Variable Calc Module Three 3-1 Module Three Discussion: Continuity and Differentiability 3-1 Module Three Discussion: Continuity and Differentiability Remaining Time: Unlimited { Module Three Discussion x + 13 if x < 8 Analyze the function f (x) = V8 x +9 if x> 8 Your classmates may be analyzing different functions, so in your initial post in Brightspace be sure to specify the function that you are analyzing. Part 1: Is f (x) continuous at x = 8? Explain why or why not in your Discussion post O Yes O No Hint: In order for f (x) to be continuous at x = 8, the limits of f (x) from the left and from the right must both exist and be equal to f (8). Part 2: Is f(x) differentiable at x = 8? Explain why or why not in your Discussion post. O Yes O No Hint: Similarly to continuity, in order for f (x) to be differentiable at x = 8, f (x) must be continuous at x =8 and the limits of the difference quotient f(8+h)-f(8) from the left and from the right must both exist and be equal to each other.
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