Simplify the trigonometric expression: sin B+ cos BcotB 4.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.3: Logarithmic Functions And Their Graphs
Problem 139E
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![## Mathematical Functions and Trigonometric Simplification
### Question 3: Graphing and Analysis of a Logarithmic Function
Consider the logarithmic function given below:
\[ f(x) = \log_2(x - 2) + 3 \]
#### Instructions:
a) **Graph the Function:**
- Plot the function \( f(x) = \log_2(x - 2) + 3 \) as accurately as possible.
- Label the scales on both the x-axis and y-axis.
- Label important points on the curve, with at least two points marked with their coordinates.
- Identify and label the domain, range, and asymptote of the function.
*Hint:* Consider the inverse of this function for better understanding.
**Domain:**
**Range:**
**Asymptote:**
\[
\begin{xy}
\includegraphics[scale=0.5]{log-graph.pdf}
\end{xy}
\]
b) **Solve:**
\[ f(x) = 4 \]
### Question 4: Trigonometric Simplification
#### Simplify the following trigonometric expression:
\[ \sin B + \cos B \cot B \]
---
#### Explanation of the Diagrams:
The diagram provided is a graph with a Cartesian coordinate system (x and y axes) subdivided into evenly spaced intervals, allowing precise plotting of the function \( f(x) \). Important features, such as the graph transition points and asymptotes, should be carefully noted and labeled for clarity. Plotting and analysis involve addressing the function's domain, range, and finding any asymptotic behavior, which will help in understanding the overall shape and properties of the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff62d5ca7-5439-4cfe-bb83-29d1381eaedb%2F5a9bd058-e64c-4476-bfee-18a25bc638ab%2Fzkeatfi_processed.png&w=3840&q=75)
Transcribed Image Text:## Mathematical Functions and Trigonometric Simplification
### Question 3: Graphing and Analysis of a Logarithmic Function
Consider the logarithmic function given below:
\[ f(x) = \log_2(x - 2) + 3 \]
#### Instructions:
a) **Graph the Function:**
- Plot the function \( f(x) = \log_2(x - 2) + 3 \) as accurately as possible.
- Label the scales on both the x-axis and y-axis.
- Label important points on the curve, with at least two points marked with their coordinates.
- Identify and label the domain, range, and asymptote of the function.
*Hint:* Consider the inverse of this function for better understanding.
**Domain:**
**Range:**
**Asymptote:**
\[
\begin{xy}
\includegraphics[scale=0.5]{log-graph.pdf}
\end{xy}
\]
b) **Solve:**
\[ f(x) = 4 \]
### Question 4: Trigonometric Simplification
#### Simplify the following trigonometric expression:
\[ \sin B + \cos B \cot B \]
---
#### Explanation of the Diagrams:
The diagram provided is a graph with a Cartesian coordinate system (x and y axes) subdivided into evenly spaced intervals, allowing precise plotting of the function \( f(x) \). Important features, such as the graph transition points and asymptotes, should be carefully noted and labeled for clarity. Plotting and analysis involve addressing the function's domain, range, and finding any asymptotic behavior, which will help in understanding the overall shape and properties of the function.
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