x + 1, x < 2 İk(x – 5)², x > 2' Consider f(x) = ,where k is some constant. 1. Sketch the graph of f for k= 1. 2. The resulting graph in (1) is discontinuous at x = 2. What does it mean for a function to be discontinuous at a point? 3. Find the limits for the original function (the one with k). a. lim f(x) = x-2- b. lim f(x) = X-2+ c. What must be true of these two limits for f to be continuous at x = с. 4. Find the value of k that makes fcontinuous at x = 2.
x + 1, x < 2 İk(x – 5)², x > 2' Consider f(x) = ,where k is some constant. 1. Sketch the graph of f for k= 1. 2. The resulting graph in (1) is discontinuous at x = 2. What does it mean for a function to be discontinuous at a point? 3. Find the limits for the original function (the one with k). a. lim f(x) = x-2- b. lim f(x) = X-2+ c. What must be true of these two limits for f to be continuous at x = с. 4. Find the value of k that makes fcontinuous at x = 2.
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...
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Transcribed Image Text:Continuity and Piecewise Functions
Objective: Given a piecewise function, find a value for a constant that will make the
function continuous.
x + 1, x < 2
Consider f (x) = {k(x – 5)², x 2 2'
,where k is some constant.
1. Sketch the graph of f for k = 1.
2. The resulting graph in (1) is discontinuous at x = 2. What does it mean for a
function to be discontinuous at a point?
3. Find the limits for the original function (the one with k).
a. lim f(x) =
X-2-
b. lim f(x) =
X-2+
c. What must be true of these two limits for f to be continuous at x = 2?
4. Find the value of k that makes fcontinuous at x = 2,
Transcribed Image Text:5. Sketch the graph of f for the value of k that you found in (4).
6. What feature does the graph have at x = 2?
7. What can you say about the slope of f at this point?
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