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)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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 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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