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Use the graph to find the following. (a) the domain of f (b) the range of f (c) the x-intercepts (d) the y-intercept (e) intervals on which f is increasing (f) intervals on which f is decreasing (g) intervals on which f is constant (h) the number at which f has a relative minimum (i) the relative minimum of f () f(-6) (k) The values of x for which f(x) = 3 (1) Is f even, odd or neither? 4- -6 12 -4-

Use the graph to find the following. (a) the domain of f (b) the range of f (c) the x-intercepts (d) the y-intercept (e) intervals on which f is increasing (f) intervals on which f is decreasing (g) intervals on which f is constant (h) the number at which f has a relative minimum (i) the relative minimum of f () f(-6) (k) The values of x for which f(x) = 3 (1) Is f even, odd or neither? 4- -6 12 -4-

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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**Analyzing Graph Functions for Educational Purposes** When studying the properties of functions using their graphs, it's essential to derive specific characteristics from the visual data presented. Below we utilize a graph to answer various questions about the function \( f \). ### Graph Description The graph depicts a parabola that opens upwards, crossing the y-axis at approximately \( y = -4 \). The vertex, which is the minimum point of this parabola, is located at \( (1, -5) \). The x-axis is crossed at two points, and the graph extends infinitely in both directions along the x-axis. ### Questions and Corresponding Answers (a) **Domain of \( f \)** The domain of a function includes all possible x-values that the function can take. For this parabola, the domain is all real numbers because it extends infinitely in both the left and right directions. - **Answer:** \( (-\infty, \infty) \) (b) **Range of \( f \)** The range consists of all possible y-values that the function can produce. The lowest point of the parabola is at \( y = -5 \) and it extends upwards infinitely. - **Answer:** \( [-5, \infty) \) (c) **X-Intercepts** X-intercepts are the points where the graph crosses the x-axis. From the graph, these points are approximately \( x = -1 \) and \( x = 3 \), where the y-value is zero. - **Answer:** \( x = -1 \) and \( x = 3 \) (d) **Y-Intercept** The y-intercept is the point where the graph crosses the y-axis. From the graph, this occurs at \( y = -4 \). - **Answer:** \( y = -4 \) (e) **Intervals on which \( f \) is Increasing** The function \( f \) is increasing on the interval where the y-value rises as the x-value increases. For this parabola, this occurs after the vertex. - **Answer:** \( (1, \infty) \) (f) **Intervals on which \( f \) is Decreasing** The function \( f \) is decreasing on the interval where the y-value drops as the x-value increases. For this parabola, this happens before the vertex. - **Answer:** \( (-\infty, 1) \) (g) **Intervals on which
Transcribed Image Text:**Analyzing Graph Functions for Educational Purposes** When studying the properties of functions using their graphs, it's essential to derive specific characteristics from the visual data presented. Below we utilize a graph to answer various questions about the function \( f \). ### Graph Description The graph depicts a parabola that opens upwards, crossing the y-axis at approximately \( y = -4 \). The vertex, which is the minimum point of this parabola, is located at \( (1, -5) \). The x-axis is crossed at two points, and the graph extends infinitely in both directions along the x-axis. ### Questions and Corresponding Answers (a) **Domain of \( f \)** The domain of a function includes all possible x-values that the function can take. For this parabola, the domain is all real numbers because it extends infinitely in both the left and right directions. - **Answer:** \( (-\infty, \infty) \) (b) **Range of \( f \)** The range consists of all possible y-values that the function can produce. The lowest point of the parabola is at \( y = -5 \) and it extends upwards infinitely. - **Answer:** \( [-5, \infty) \) (c) **X-Intercepts** X-intercepts are the points where the graph crosses the x-axis. From the graph, these points are approximately \( x = -1 \) and \( x = 3 \), where the y-value is zero. - **Answer:** \( x = -1 \) and \( x = 3 \) (d) **Y-Intercept** The y-intercept is the point where the graph crosses the y-axis. From the graph, this occurs at \( y = -4 \). - **Answer:** \( y = -4 \) (e) **Intervals on which \( f \) is Increasing** The function \( f \) is increasing on the interval where the y-value rises as the x-value increases. For this parabola, this occurs after the vertex. - **Answer:** \( (1, \infty) \) (f) **Intervals on which \( f \) is Decreasing** The function \( f \) is decreasing on the interval where the y-value drops as the x-value increases. For this parabola, this happens before the vertex. - **Answer:** \( (-\infty, 1) \) (g) **Intervals on which
**Mathematical Functions and Their Graphs** **Instructions:** Use the provided graph to answer the following questions. *Graph Analysis:* The graph shown is a quadratic function \(f(x)\) which is a downward-facing parabola. It intersects the x-axis at two points and the y-axis at one point. The vertex of the parabola represents the minimum value of the function. *Questions:* 1. (a) **Find the domain of \( f \).** 2. (b) **Find the range of \( f \).** 3. (c) **Identify the x-intercepts.** 4. (d) **Identify the y-intercept.** 5. (e) **Determine the intervals on which \( f \) is increasing.** 6. (f) **Determine the intervals on which \( f \) is decreasing.** 7. (g) **Identify any intervals on which \( f \) is constant.** 8. (h) **Find the number at which \( f \) has a relative minimum.** 9. (i) **Calculate the relative minimum of \( f \).** 10. (j) **Compute \( f(-6) \).** 11. (k) **Determine the values of \( x \) for which \( f(x) = 3 \).** 12. (l) **State whether \( f \) is even, odd, or neither.** Specific Questions: - (j) **What is \( f(-6) \)?** \( f(-6) = \) [Your answer] - (k) **What are the x-values where \( f(x) = 3 \)? The leftmost x-value where \( f(x) = 3 \) is when \( x = 1 \). What is the rightmost x-value where \( f(x) = 3 \)?** \( x = \) [Your answer] - (l) **Is \( f \) even, odd, or neither?** [Select the appropriate option] **Graph Details:** The graph is a standard Cartesian coordinate system with the x-axis ranging from -6 to 12 and the y-axis ranging from -4 to 6. The vertex of the graph is located at the point (0, 0), indicating that this is the relative minimum of the function. The parabola
Transcribed Image Text:**Mathematical Functions and Their Graphs** **Instructions:** Use the provided graph to answer the following questions. *Graph Analysis:* The graph shown is a quadratic function \(f(x)\) which is a downward-facing parabola. It intersects the x-axis at two points and the y-axis at one point. The vertex of the parabola represents the minimum value of the function. *Questions:* 1. (a) **Find the domain of \( f \).** 2. (b) **Find the range of \( f \).** 3. (c) **Identify the x-intercepts.** 4. (d) **Identify the y-intercept.** 5. (e) **Determine the intervals on which \( f \) is increasing.** 6. (f) **Determine the intervals on which \( f \) is decreasing.** 7. (g) **Identify any intervals on which \( f \) is constant.** 8. (h) **Find the number at which \( f \) has a relative minimum.** 9. (i) **Calculate the relative minimum of \( f \).** 10. (j) **Compute \( f(-6) \).** 11. (k) **Determine the values of \( x \) for which \( f(x) = 3 \).** 12. (l) **State whether \( f \) is even, odd, or neither.** Specific Questions: - (j) **What is \( f(-6) \)?** \( f(-6) = \) [Your answer] - (k) **What are the x-values where \( f(x) = 3 \)? The leftmost x-value where \( f(x) = 3 \) is when \( x = 1 \). What is the rightmost x-value where \( f(x) = 3 \)?** \( x = \) [Your answer] - (l) **Is \( f \) even, odd, or neither?** [Select the appropriate option] **Graph Details:** The graph is a standard Cartesian coordinate system with the x-axis ranging from -6 to 12 and the y-axis ranging from -4 to 6. The vertex of the graph is located at the point (0, 0), indicating that this is the relative minimum of the function. The parabola
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