Use the graph below to determine which of the following is the best approximation of the solutions of the equation f(x) = g(x). Question 3 options: x = -0.5, x = 2.5 x = 1, x = 3 x = 0.5, x = 4.5 x = -1, x = 5 ### Understanding and Interpreting the Graphs of \( f(x) \) and \( g(x) \)The graph above displays two functions: \( f(x) \) and \( g(x) \), each represented by distinct curves.#### Function \( f(x) \):- **Type**: Linear function.- **Equation**: The exact equation is not provided, but based on the visual representation, \( f(x) \) is a straight line.- **Slope**: The line appears to have a negative slope, indicating that as \( x \) increases, \( y \) decreases.- **Intersection with Y-Axis**: The line intersects the y-axis at approximately \( y = 6 \).- **Crossing Points**: \( f(x) \) crosses the x-axis at approximately \( x = -3 \).#### Function \( g(x) \):- **Type**: Polynomial function (likely quadratic).- **Equation**: While the specific equation is not given, \( g(x) \) is a parabola opening downward.- **Vertex**: The peak point (vertex) of the parabola is near \( (3, 5) \).- **Intercepts**: - **Y-Intercept**: The graph of \( g(x) \) intersects the y-axis at \( y = 0 \). - **X-Intercepts**: The parabola intersects the x-axis at approximately \( x = 0 \) and \( x = 6 \).- **Turning Point**: The turning point is at the vertex \( (3, 5) \), indicating the maximum value of \( g(x) \) at \( y = 5 \).#### Intersection Points:- There are two intersections between \( f(x) \) and \( g(x) \): - The first intersection is near \( (1, 1) \). - The second intersection occurs around \( (5, -1) \).### Axes and Grid Details:- **Axes**: - The horizontal axis represents the \( x \)-values, ranging from -6 to 6. - The vertical axis represents the \( y \)-values, ranging from -6 to 6.- **Grid**: The background grid helps in approximating the coordinates of various points on the graph. #### Analyzing the Functions Together:- Overlapping these graphs allows

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Answered: -6. f(x) Z g(x) T 6 x 8

Math

Algebra

-6. f(x) Z g(x) T 6 x 8

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

Use the graph below to determine which of the following is the best approximation of the solutions of the equation f(x) = g(x).

Question 3 options:

	x = -0.5, x = 2.5
	x = 1, x = 3
	x = 0.5, x = 4.5
	x = -1, x = 5

### Understanding and Interpreting the Graphs of \( f(x) \) and \( g(x) \)

The graph above displays two functions: \( f(x) \) and \( g(x) \), each represented by distinct curves.

#### Function \( f(x) \):
- **Type**: Linear function.
- **Equation**: The exact equation is not provided, but based on the visual representation, \( f(x) \) is a straight line.
- **Slope**: The line appears to have a negative slope, indicating that as \( x \) increases, \( y \) decreases.
- **Intersection with Y-Axis**: The line intersects the y-axis at approximately \( y = 6 \).
- **Crossing Points**: \( f(x) \) crosses the x-axis at approximately \( x = -3 \).

#### Function \( g(x) \):
- **Type**: Polynomial function (likely quadratic).
- **Equation**: While the specific equation is not given, \( g(x) \) is a parabola opening downward.
- **Vertex**: The peak point (vertex) of the parabola is near \( (3, 5) \).
- **Intercepts**:
- **Y-Intercept**: The graph of \( g(x) \) intersects the y-axis at \( y = 0 \).
- **X-Intercepts**: The parabola intersects the x-axis at approximately \( x = 0 \) and \( x = 6 \).
- **Turning Point**: The turning point is at the vertex \( (3, 5) \), indicating the maximum value of \( g(x) \) at \( y = 5 \).

#### Intersection Points:
- There are two intersections between \( f(x) \) and \( g(x) \):
- The first intersection is near \( (1, 1) \).
- The second intersection occurs around \( (5, -1) \).

### Axes and Grid Details:
- **Axes**:
- The horizontal axis represents the \( x \)-values, ranging from -6 to 6.
- The vertical axis represents the \( y \)-values, ranging from -6 to 6.
- **Grid**: The background grid helps in approximating the coordinates of various points on the graph.

#### Analyzing the Functions Together:
- Overlapping these graphs allows

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