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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Question
Q12. Please answer all the parts to this question
![The image presents a mathematical problem requiring the determination of specific values for the variables \( a \) and \( b \) to ensure that the function \( f(x) \) is continuous across its entire domain. The function \( f(x) \) is defined piecewise as follows:
\[
f(x) =
\begin{cases}
\dfrac{x^2 - 4}{x - 2} & \text{if } x < 2 \\
ax^2 - bx + 3 & \text{if } 2 \leq x < 3 \\
4x - a + b & \text{if } x \geq 3
\end{cases}
\]
There are also blank spaces provided to fill in the values of \( a \) and \( b \):
\[
a = \_\_\_\_
\]
\[
b = \_\_\_\_
\]
The goal is to solve for \( a \) and \( b \) such that \( f(x) \) is continuous everywhere.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b1f7975-4b0c-45ff-85b5-d245674b95f7%2F4c48f30a-534c-4256-a252-5edd1dec1b3c%2F48sfwz_processed.png&w=3840&q=75)
Transcribed Image Text:The image presents a mathematical problem requiring the determination of specific values for the variables \( a \) and \( b \) to ensure that the function \( f(x) \) is continuous across its entire domain. The function \( f(x) \) is defined piecewise as follows:
\[
f(x) =
\begin{cases}
\dfrac{x^2 - 4}{x - 2} & \text{if } x < 2 \\
ax^2 - bx + 3 & \text{if } 2 \leq x < 3 \\
4x - a + b & \text{if } x \geq 3
\end{cases}
\]
There are also blank spaces provided to fill in the values of \( a \) and \( b \):
\[
a = \_\_\_\_
\]
\[
b = \_\_\_\_
\]
The goal is to solve for \( a \) and \( b \) such that \( f(x) \) is continuous everywhere.
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