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The graphs of f(x) and g(x) have an intercept in common. What is the ordered pair of the intercept?

The graphs of f(x) and g(x) have an intercept in common. What is the ordered pair of the intercept?

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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Question

The graphs of f(x) and g(x) have an intercept in common. What is the ordered pair of the intercept? 

The image shows four options, each with a radio button next to a pair of coordinates: 1. \((0, -1)\) 2. \((-1, 0)\) 3. \((0, 2)\) 4. \((2, 0)\) These options might be used to select a specific point on a Cartesian plane. Each coordinate pair consists of an \(x\)-value and a \(y\)-value in the form \((x, y)\).
Transcribed Image Text:The image shows four options, each with a radio button next to a pair of coordinates: 1. \((0, -1)\) 2. \((-1, 0)\) 3. \((0, 2)\) 4. \((2, 0)\) These options might be used to select a specific point on a Cartesian plane. Each coordinate pair consists of an \(x\)-value and a \(y\)-value in the form \((x, y)\).
The image is a graph that features two functions, \( g(x) \) and \( f(x) \), plotted on a coordinate plane. Additionally, there is a horizontal dashed line labeled \( y = 1 \). ### Graph Details: 1. **Axes and Grid:** - The graph is set on a coordinate system with the x-axis ranging from -6 to 6 and the y-axis from -3 to 9. - There are grid lines aiding in determining the values of the functions at various points. 2. **Function \( g(x) \):** - The curve for \( g(x) \) appears to be an exponential function that rises steeply as \( x \) increases. - It passes through the point (0, 2), indicating that at \( x = 0 \), \( g(x) = 2 \). - As \( x \) becomes more negative, \( g(x) \) approaches 0, suggesting it may have a horizontal asymptote near the x-axis. 3. **Function \( f(x) \):** - The curve for \( f(x) \) appears to be a linear function with a negative slope. - It crosses the x-axis at approximately (1, 0) and the y-axis at (0, -2). 4. **Line \( y = 1 \):** - A dashed horizontal line at \( y = 1 \) runs parallel to the x-axis. - This line provides a reference for comparison with the values of \( g(x) \) and \( f(x) \). ### Key Observations: - Both functions intersect the horizontal line \( y = 1 \) at different \( x \) values. - The graph showcases the intersection of different function types (exponential and linear) with the horizontal line, illustrating concepts of function behavior and intersection points.
Transcribed Image Text:The image is a graph that features two functions, \( g(x) \) and \( f(x) \), plotted on a coordinate plane. Additionally, there is a horizontal dashed line labeled \( y = 1 \). ### Graph Details: 1. **Axes and Grid:** - The graph is set on a coordinate system with the x-axis ranging from -6 to 6 and the y-axis from -3 to 9. - There are grid lines aiding in determining the values of the functions at various points. 2. **Function \( g(x) \):** - The curve for \( g(x) \) appears to be an exponential function that rises steeply as \( x \) increases. - It passes through the point (0, 2), indicating that at \( x = 0 \), \( g(x) = 2 \). - As \( x \) becomes more negative, \( g(x) \) approaches 0, suggesting it may have a horizontal asymptote near the x-axis. 3. **Function \( f(x) \):** - The curve for \( f(x) \) appears to be a linear function with a negative slope. - It crosses the x-axis at approximately (1, 0) and the y-axis at (0, -2). 4. **Line \( y = 1 \):** - A dashed horizontal line at \( y = 1 \) runs parallel to the x-axis. - This line provides a reference for comparison with the values of \( g(x) \) and \( f(x) \). ### Key Observations: - Both functions intersect the horizontal line \( y = 1 \) at different \( x \) values. - The graph showcases the intersection of different function types (exponential and linear) with the horizontal line, illustrating concepts of function behavior and intersection points.
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