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f(x)=√√√√x+2 -9-8-7-6-5-4-3-2-19 -1 -2 -3 -4 -5 -6 -7 -8 -9 1234 hich statement about these two functions is true? OA) Both functions have the same maximum value. OB) Both functions have the same domain. OC) Both functions have a y-intercept of 2.

f(x)=√√√√x+2 -9-8-7-6-5-4-3-2-19 -1 -2 -3 -4 -5 -6 -7 -8 -9 1234 hich statement about these two functions is true? OA) Both functions have the same maximum value. OB) Both functions have the same domain. OC) Both functions have a y-intercept of 2.

Algebra and Trigonometry (6th Edition)
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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**Comparing Two Functions** In this section, we will compare two functions, labeled Function I and Function II, and analyze their properties. ### Function I The equation for Function I is given by: \[ f(x) = \sqrt{x} + 2 \] ### Function II For Function II, a graph is provided: - The y-axis and x-axis range from -9 to 9. - The graph of Function II shows a curve that starts at the point (0, 2) and gradually decreases towards the x-axis as x increases. - Observing the graph, the curve never touches or crosses the x-axis and approaches y=0 asymptotically. ### Question: **Which statement about these two functions is true?** A. Both functions have the same maximum value. B. Both functions have the same domain. C. Both functions have a y-intercept of 2. D. All of the above. **Explanation:** 1. **For option A**: Function I does not have a maximum value as it increases without bound as x increases. On the other hand, Function II seems to approach a horizontal asymptote as y approaches 0 and does not have a maximum value either. 2. **For option B**: The domain of Function I is \(x \geq 0\) since the square root function is undefined for negative values of x. For Function II, the graph starts at x = 0 and extends to positive infinity, which implies both functions have the same domain. 3. **For option C**: Both functions intersect the y-axis at (0, 2), indicating they have a y-intercept of 2. **Correct Answer:** - **B. Both functions have the same domain.** - **C. Both functions have a y-intercept of 2.** But since both B and C are true, the correct answer is: - **D. All of the above.**
Transcribed Image Text:**Comparing Two Functions** In this section, we will compare two functions, labeled Function I and Function II, and analyze their properties. ### Function I The equation for Function I is given by: \[ f(x) = \sqrt{x} + 2 \] ### Function II For Function II, a graph is provided: - The y-axis and x-axis range from -9 to 9. - The graph of Function II shows a curve that starts at the point (0, 2) and gradually decreases towards the x-axis as x increases. - Observing the graph, the curve never touches or crosses the x-axis and approaches y=0 asymptotically. ### Question: **Which statement about these two functions is true?** A. Both functions have the same maximum value. B. Both functions have the same domain. C. Both functions have a y-intercept of 2. D. All of the above. **Explanation:** 1. **For option A**: Function I does not have a maximum value as it increases without bound as x increases. On the other hand, Function II seems to approach a horizontal asymptote as y approaches 0 and does not have a maximum value either. 2. **For option B**: The domain of Function I is \(x \geq 0\) since the square root function is undefined for negative values of x. For Function II, the graph starts at x = 0 and extends to positive infinity, which implies both functions have the same domain. 3. **For option C**: Both functions intersect the y-axis at (0, 2), indicating they have a y-intercept of 2. **Correct Answer:** - **B. Both functions have the same domain.** - **C. Both functions have a y-intercept of 2.** But since both B and C are true, the correct answer is: - **D. All of the above.**
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