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Find all the X-values that make the function positive (f(x) > 0 when x =? ). Enter your answer in interval notation. Enter -0 as -INF, ∞ as INF, and U (union) as U. If none exist, type none. f(x) > 0 when x is : Submit Answer Tries 0/99 Find all the X-values that make the function negative (f(x) < 0 when x =? ). Enter your answer in interval notation. Enter -o as -INF, ∞ as INF, and U (union) as U. If none exist, type none. f(x) < 0 when x is :

Find all the X-values that make the function positive (f(x) > 0 when x =? ). Enter your answer in interval notation. Enter -0 as -INF, ∞ as INF, and U (union) as U. If none exist, type none. f(x) > 0 when x is : Submit Answer Tries 0/99 Find all the X-values that make the function negative (f(x) < 0 when x =? ). Enter your answer in interval notation. Enter -o as -INF, ∞ as INF, and U (union) as U. If none exist, type none. f(x) < 0 when x is :

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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This is a graph of the exponential function \( y = e^x \), where \( e \) is the base of the natural logarithm, approximately equal to 2.71828. The graph is a smooth curve that rapidly increases as the value of \( x \) increases. **Key Features of the Graph:** - **Axes**: The horizontal axis represents the \( x \)-values, and the vertical axis represents the \( y \)-values. - **Behavior as \( x \) increases**: The graph rises steeply, demonstrating exponential growth. - **Behavior as \( x \) decreases**: As \( x \) becomes more negative, the graph approaches but never quite reaches the \( x \)-axis (approaches zero). - **Intercept**: The curve passes through the point (0, 1), indicating that when \( x = 0 \), \( e^x = 1 \). - **Symmetry**: There is no symmetry about the axes, but the function is increasing for all real numbers. This graph is a classic example of an exponential curve, often seen in contexts such as population growth, compound interest, and natural processes.
Transcribed Image Text:This is a graph of the exponential function \( y = e^x \), where \( e \) is the base of the natural logarithm, approximately equal to 2.71828. The graph is a smooth curve that rapidly increases as the value of \( x \) increases. **Key Features of the Graph:** - **Axes**: The horizontal axis represents the \( x \)-values, and the vertical axis represents the \( y \)-values. - **Behavior as \( x \) increases**: The graph rises steeply, demonstrating exponential growth. - **Behavior as \( x \) decreases**: As \( x \) becomes more negative, the graph approaches but never quite reaches the \( x \)-axis (approaches zero). - **Intercept**: The curve passes through the point (0, 1), indicating that when \( x = 0 \), \( e^x = 1 \). - **Symmetry**: There is no symmetry about the axes, but the function is increasing for all real numbers. This graph is a classic example of an exponential curve, often seen in contexts such as population growth, compound interest, and natural processes.
The image contains two sections, each asking for specific X-values based on the positivity or negativity of a function. **Section 1:** - **Instruction:** "Find all the X-values that make the function positive \((f(x) > 0 \text{ when } x = ?)\). Enter your answer in interval notation." - **Guidelines for Input:** Enter \(-\infty\) as -INF, \(\infty\) as INF, and \(\cup\) (union) as U. If none exist, type `none`. - **Expression to Solve:** \(f(x) > 0 \text{ when } x \text{ is: }\) - **Answer Input Box:** A text box is provided for input. - **Button:** "Submit Answer" with an attempt counter showing "Tries 0/99." **Section 2:** - **Instruction:** "Find all the X-values that make the function negative \((f(x) < 0 \text{ when } x = ?)\). Enter your answer in interval notation." - **Guidelines for Input:** Enter \(-\infty\) as -INF, \(\infty\) as INF, and \(\cup\) (union) as U. If none exist, type `none`. - **Expression to Solve:** \(f(x) < 0 \text{ when } x \text{ is: }\) - **Answer Input Box:** A text box is provided for input. - **Button:** "Submit Answer" with an attempt counter showing "Tries 0/99." There are no graphs or diagrams involved; the content is focused on determining interval notation solutions for the conditions given.
Transcribed Image Text:The image contains two sections, each asking for specific X-values based on the positivity or negativity of a function. **Section 1:** - **Instruction:** "Find all the X-values that make the function positive \((f(x) > 0 \text{ when } x = ?)\). Enter your answer in interval notation." - **Guidelines for Input:** Enter \(-\infty\) as -INF, \(\infty\) as INF, and \(\cup\) (union) as U. If none exist, type `none`. - **Expression to Solve:** \(f(x) > 0 \text{ when } x \text{ is: }\) - **Answer Input Box:** A text box is provided for input. - **Button:** "Submit Answer" with an attempt counter showing "Tries 0/99." **Section 2:** - **Instruction:** "Find all the X-values that make the function negative \((f(x) < 0 \text{ when } x = ?)\). Enter your answer in interval notation." - **Guidelines for Input:** Enter \(-\infty\) as -INF, \(\infty\) as INF, and \(\cup\) (union) as U. If none exist, type `none`. - **Expression to Solve:** \(f(x) < 0 \text{ when } x \text{ is: }\) - **Answer Input Box:** A text box is provided for input. - **Button:** "Submit Answer" with an attempt counter showing "Tries 0/99." There are no graphs or diagrams involved; the content is focused on determining interval notation solutions for the conditions given.
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