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e graph of f to determine each of the following. domain of f range of f zero(s) of f e intervals on which f is increasing

e graph of f to determine each of the following. domain of f range of f zero(s) of f e intervals on which f is increasing

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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Use the graph of \( f \) to determine each of the following: (a) the domain of \( f \) (b) the range of \( f \) (c) the zero(s) of \( f \) (d) \(f(-1)\) (e) the intervals on which \( f \) is increasing (f) the intervals on which \( f \) is decreasing (g) the values for which \( f(x) \leq 0 \) (h) any relative maxima or minima (i) the value(s) of \( x \) for which \( f(x) = -4 \) (j) Is \( f(4) \) positive or negative? ### Explanation of the Graph: The graph of \( f \) appears to be a parabola that opens downwards. The vertex of the parabola indicates the maximum value of the function. The x-axis ranges from -10 to 10, while the y-axis ranges from -6 to 6. ### Detailed Description: - **Domain** refers to all possible input values (x-values) for the function \( f \). - **Range** refers to all possible output values (y-values) for the function \( f \). - **Zeros of \( f \)** are the x-values where \( f(x) = 0 \), meaning where the graph intersects the x-axis. - **\( f(-1) \)** is the y-value when \( x = -1 \). - **Intervals of increase** are the x-values where the function is increasing as you move from left to right. - **Intervals of decrease** are the x-values where the function is decreasing as you move from left to right. - **Values for which \( f(x) \leq 0 \)** are the x-values where the graph is below or on the x-axis. - **Relative maxima or minima** are the highest or lowest points in the vicinity of the vertex of the graph. - **Values of \( x \) for which \( f(x) = -4 \)** are the x-values where the graph intersects the line \( y = -4 \). - **\( f(4) \)** refers to determining whether the y-value at \( x = 4 \) is positive or negative. By analyzing the graph, you can determine the specific values for each question.
Transcribed Image Text:Use the graph of \( f \) to determine each of the following: (a) the domain of \( f \) (b) the range of \( f \) (c) the zero(s) of \( f \) (d) \(f(-1)\) (e) the intervals on which \( f \) is increasing (f) the intervals on which \( f \) is decreasing (g) the values for which \( f(x) \leq 0 \) (h) any relative maxima or minima (i) the value(s) of \( x \) for which \( f(x) = -4 \) (j) Is \( f(4) \) positive or negative? ### Explanation of the Graph: The graph of \( f \) appears to be a parabola that opens downwards. The vertex of the parabola indicates the maximum value of the function. The x-axis ranges from -10 to 10, while the y-axis ranges from -6 to 6. ### Detailed Description: - **Domain** refers to all possible input values (x-values) for the function \( f \). - **Range** refers to all possible output values (y-values) for the function \( f \). - **Zeros of \( f \)** are the x-values where \( f(x) = 0 \), meaning where the graph intersects the x-axis. - **\( f(-1) \)** is the y-value when \( x = -1 \). - **Intervals of increase** are the x-values where the function is increasing as you move from left to right. - **Intervals of decrease** are the x-values where the function is decreasing as you move from left to right. - **Values for which \( f(x) \leq 0 \)** are the x-values where the graph is below or on the x-axis. - **Relative maxima or minima** are the highest or lowest points in the vicinity of the vertex of the graph. - **Values of \( x \) for which \( f(x) = -4 \)** are the x-values where the graph intersects the line \( y = -4 \). - **\( f(4) \)** refers to determining whether the y-value at \( x = 4 \) is positive or negative. By analyzing the graph, you can determine the specific values for each question.
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