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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Only question #1, please show detailed steps.
![**Calculus Sample Practice Problems for Calculus Test #1: Material up to Implicit Differentiation**
**Section I: PreCalc Review**
While there will not be problems like this on the test, some problems require particular skills.
1) Find the domain of the function \( f(x) = \frac{\sqrt{3-x}}{x+4} \)
2) Sketch the graph of \( f(x) = \begin{cases}
2x - 3 & 0 \leq x < 3 \\
1 & x = 3 \\
5-x & x > 3
\end{cases} \)
3) If \( f(x) = 5x + 4 \) and \( g(x) = 7 - 2x \), what does \( (f \circ g)(x) \) equal?
4) If \( ABC \) is a right triangle with the right angle at \( C \), then find \( a \).
5) Use translations to sketch the graph of \( y = \frac{1}{f(x+1)} \) given that...
[The rest of the sentence is obscured in the image]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10b1f275-2c41-4985-b23a-aa3382c0d493%2F1aafecdf-3a60-4a8d-a44b-6f40fd63ad56%2F8m0zbem_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculus Sample Practice Problems for Calculus Test #1: Material up to Implicit Differentiation**
**Section I: PreCalc Review**
While there will not be problems like this on the test, some problems require particular skills.
1) Find the domain of the function \( f(x) = \frac{\sqrt{3-x}}{x+4} \)
2) Sketch the graph of \( f(x) = \begin{cases}
2x - 3 & 0 \leq x < 3 \\
1 & x = 3 \\
5-x & x > 3
\end{cases} \)
3) If \( f(x) = 5x + 4 \) and \( g(x) = 7 - 2x \), what does \( (f \circ g)(x) \) equal?
4) If \( ABC \) is a right triangle with the right angle at \( C \), then find \( a \).
5) Use translations to sketch the graph of \( y = \frac{1}{f(x+1)} \) given that...
[The rest of the sentence is obscured in the image]
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