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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![**Question 4**
A continuous function has a domain of \(-7 \leq x \leq 10\) and has selected values shown in the table below. The function has exactly two zeroes and a relative maximum at \((-4, 12)\) and a relative minimum at \( (5, -6)\).
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
x & -7 & -4 & -1 & 0 & 2 & 5 & 7 & 10 \\
\hline
f(x) & 8 & 12 & 0 & -2 & -5 & -6 & 0 & 4 \\
\hline
\end{array}
\]
(a) State the interval on which \( f(x) \) is decreasing.
(b) State the interval over which \( f(x) < 0 \).
**Explanation:**
- The table provides specific values of the function \( f(x) \) at different points \( x \) within the domain \([-7, 10]\).
- **Decreasing intervals:** The function is said to be decreasing where the function values drop as \( x \) increases.
**Observing the table**:
- From \( x = -4 \) to \( x = 5 \), \( f(x) \) decreases from 12 to -6.
- From \( x = 7 \) to \( x = 10 \), \( f(x) \) increases from 0 to 4.
Thus, \( f(x) \) is decreasing in the interval \([-4, 5]\).
- **Negative intervals:** The function \( f(x) \) is negative where the values of \( f(x) \) are less than zero.
**Observing the table**:
- \( f(x) \) is negative between \( x = -1 \) and \( x = 7 \).
Therefore, \( f(x) < 0 \) in the interval \([-1, 7]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F332b9bd1-1c62-4afe-9ed5-7dc63aa5060b%2F9757e517-63cd-426b-a13d-631e2568b452%2Fhmn2n1u_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 4**
A continuous function has a domain of \(-7 \leq x \leq 10\) and has selected values shown in the table below. The function has exactly two zeroes and a relative maximum at \((-4, 12)\) and a relative minimum at \( (5, -6)\).
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
x & -7 & -4 & -1 & 0 & 2 & 5 & 7 & 10 \\
\hline
f(x) & 8 & 12 & 0 & -2 & -5 & -6 & 0 & 4 \\
\hline
\end{array}
\]
(a) State the interval on which \( f(x) \) is decreasing.
(b) State the interval over which \( f(x) < 0 \).
**Explanation:**
- The table provides specific values of the function \( f(x) \) at different points \( x \) within the domain \([-7, 10]\).
- **Decreasing intervals:** The function is said to be decreasing where the function values drop as \( x \) increases.
**Observing the table**:
- From \( x = -4 \) to \( x = 5 \), \( f(x) \) decreases from 12 to -6.
- From \( x = 7 \) to \( x = 10 \), \( f(x) \) increases from 0 to 4.
Thus, \( f(x) \) is decreasing in the interval \([-4, 5]\).
- **Negative intervals:** The function \( f(x) \) is negative where the values of \( f(x) \) are less than zero.
**Observing the table**:
- \( f(x) \) is negative between \( x = -1 \) and \( x = 7 \).
Therefore, \( f(x) < 0 \) in the interval \([-1, 7]\).
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