Find the values of a and b that make f continuous everywhere. x² - 4 X-2 f(x) = = ax² - bx + 1 4x = a + b if x < 2 if 2 < x < 3 if x ≥ 3

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section: Chapter Questions
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Find the values of a and b that make f continuous everywhere.
x² 4
X - 2
a
b =
f(x) =
ax² - bx + 1
4x = a + b
if x < 2
if 2 ≤ x < 3
if x ≥ 3
Transcribed Image Text:Find the values of a and b that make f continuous everywhere. x² 4 X - 2 a b = f(x) = ax² - bx + 1 4x = a + b if x < 2 if 2 ≤ x < 3 if x ≥ 3
Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with f for x + a and is continuous at a. (If an answer does not exist,
enter DNE.)
(a)
1
X - 1
The discontinuity is removable.
The discontinuity is not removable.
(b)
f(x) = x4
g(x) =
g(x) =
7
f(x) = x³ – x² – 72x, a = 9
x - 9
The discontinuity is removable.
The discontinuity is not removable.
a = 1
g(x) =
(c)
f(x) = [[sin(x)]], a = π (Recall that [h(x)] means the largest integer that is less than or equal to h(x).)
The discontinuity is removable.
O The discontinuity is not removable.
Transcribed Image Text:Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with f for x + a and is continuous at a. (If an answer does not exist, enter DNE.) (a) 1 X - 1 The discontinuity is removable. The discontinuity is not removable. (b) f(x) = x4 g(x) = g(x) = 7 f(x) = x³ – x² – 72x, a = 9 x - 9 The discontinuity is removable. The discontinuity is not removable. a = 1 g(x) = (c) f(x) = [[sin(x)]], a = π (Recall that [h(x)] means the largest integer that is less than or equal to h(x).) The discontinuity is removable. O The discontinuity is not removable.
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