Which of the following is true of the exponential function y=(1/3)*6^x. Choose all that apply. y-intercept is 1/3. constant ratio is 1/3. O y-intercept is 6. the graph is below constant ratio is 6. the graph isbelow
Which of the following is true of the exponential function y=(1/3)*6^x. Choose all that apply. y-intercept is 1/3. constant ratio is 1/3. O y-intercept is 6. the graph is below constant ratio is 6. the graph isbelow
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Understanding Exponential Functions
**Question:**
Which of the following is true of the exponential function \( y = \left(\frac{1}{3}\right) \cdot 6^x \)? Choose all that apply.
**Options:**
1. \[\] \(y\)-intercept is \( \frac{1}{3} \).
2. \[\] Constant ratio is \( \frac{1}{3} \).
3. \[\] \(y\)-intercept is \( 6 \).
4. \[\] The graph is below:
5. \[\] Constant ratio is \( 6 \).
6. \[\] The graph is below:
### Explanation of Graphs
**Graph 1:**
Graph 1 displays an exponential function where the curve starts from a point below the origin and rises steeply as \(x\) increases. It shows an upward trajectory, indicating a rapid increase in \(y\) values for corresponding \(x\) values.
**Graph 2:**
Graph 2 shows another exponential curve, but this one rises much steeper than the first, indicating a very rapid increase in \(y\) values as \(x\) increases. The initial part of the curve is relatively flat but quickly moves upwards.
### Selecting the Correct Answers
To correctly determine the true statements about the function \( y = \left(\frac{1}{3}\right) \cdot 6^x \):
- **Intercept Calculation:**
- When \( x = 0 \):
\[
y = \left(\frac{1}{3}\right) \cdot 6^0 = \left(\frac{1}{3}\right) \cdot 1 = \frac{1}{3}
\]
- Thus, the y-intercept is \( \frac{1}{3} \).
- **Constant Ratio:**
- The constant ratio in exponential functions of the form \( y = ab^x \) is the base \( b \). Here, the base \( b = 6 \), therefore the constant ratio is \( 6 \).
### Correct Options
Therefore, the correct](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F541e9811-c8f1-44f7-9808-3fa399aa819f%2Fe63a8f63-e674-4b75-bc69-84ac772eae35%2Fwezgee9_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Exponential Functions
**Question:**
Which of the following is true of the exponential function \( y = \left(\frac{1}{3}\right) \cdot 6^x \)? Choose all that apply.
**Options:**
1. \[\] \(y\)-intercept is \( \frac{1}{3} \).
2. \[\] Constant ratio is \( \frac{1}{3} \).
3. \[\] \(y\)-intercept is \( 6 \).
4. \[\] The graph is below:
5. \[\] Constant ratio is \( 6 \).
6. \[\] The graph is below:
### Explanation of Graphs
**Graph 1:**
Graph 1 displays an exponential function where the curve starts from a point below the origin and rises steeply as \(x\) increases. It shows an upward trajectory, indicating a rapid increase in \(y\) values for corresponding \(x\) values.
**Graph 2:**
Graph 2 shows another exponential curve, but this one rises much steeper than the first, indicating a very rapid increase in \(y\) values as \(x\) increases. The initial part of the curve is relatively flat but quickly moves upwards.
### Selecting the Correct Answers
To correctly determine the true statements about the function \( y = \left(\frac{1}{3}\right) \cdot 6^x \):
- **Intercept Calculation:**
- When \( x = 0 \):
\[
y = \left(\frac{1}{3}\right) \cdot 6^0 = \left(\frac{1}{3}\right) \cdot 1 = \frac{1}{3}
\]
- Thus, the y-intercept is \( \frac{1}{3} \).
- **Constant Ratio:**
- The constant ratio in exponential functions of the form \( y = ab^x \) is the base \( b \). Here, the base \( b = 6 \), therefore the constant ratio is \( 6 \).
### Correct Options
Therefore, the correct
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