Which Equation Represents the Function Graphed on the Coordinate Plane?

Have you ever looked at a graph and wondered what equation it represents? Maybe you were trying to solve a math problem, or maybe you were just curious. Whatever the reason, figuring out which equation represents a graph can be a challenge. But it’s not impossible! In this article, we’ll walk you through the process of finding the equation of a graph, step-by-step. We’ll start by discussing the different types of graphs and the different ways to represent them mathematically. Then, we’ll show you how to use each of these methods to find the equation of a graph. By the end of this article, you’ll be able to find the equation of any graph you come across!

“`html

Equation	Graph	Description
y = x		A linear function is a function whose graph is a straight line.
y = x^2		A quadratic function is a function whose graph is a parabola.
y = e^x		An exponential function is a function whose graph is a curve that grows exponentially.

“`

In this tutorial, we will learn how to determine which equation represents a function graphed on the coordinate plane. We will first discuss the domain and range of a function, and then we will show how to find the equation of a function given its graph.

Determining the Function’s Domain and Range

The domain of a function is the set of all possible input values, and the range is the set of all possible output values. To determine the domain and range of a function graphed on the coordinate plane, we can use the following steps:

1. Identify the x-intercepts of the graph. The x-intercepts are the points where the graph crosses the x-axis. The domain of the function is all real numbers except for the x-values of the x-intercepts.
2. Identify the y-intercept of the graph. The y-intercept is the point where the graph crosses the y-axis. The range of the function is all real numbers greater than or equal to the y-value of the y-intercept.

For example, consider the following graph of the function $f(x) = x^2$:

The x-intercepts of this graph are -1 and 1. Therefore, the domain of the function is all real numbers except -1 and 1. The y-intercept of this graph is 0. Therefore, the range of the function is all real numbers greater than or equal to 0.

Finding the Equation of a Function Given Its Graph

Once we have determined the domain and range of a function, we can find the equation of the function by using the following steps:

1. Find the slope of the graph. The slope of the graph is the change in the y-value divided by the change in the x-value as we move from one point on the graph to another.
2. Find the y-intercept of the graph. The y-intercept is the point where the graph crosses the y-axis.

Once we have the slope and the y-intercept of the graph, we can write the equation of the function in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

For example, consider the following graph of the function $f(x) = x^2$:

The slope of this graph is 2. The y-intercept of this graph is 0. Therefore, the equation of the function is $y = 2x$.

In this tutorial, we learned how to determine which equation represents a function graphed on the coordinate plane. We first discussed the domain and range of a function, and then we showed how to find the equation of a function given its graph.

By understanding the domain and range of a function, we can better understand the behavior of the function. By finding the equation of a function, we can use the function to make predictions about future values.

Additional Resources

• [Domain and Range of a Function](https://www.khanacademy.org/math/algebra/functions-and-graphs/graphing-functions/a/domain-and-range-of-a-function)
• [Finding the Equation of a Function Given Its Graph](https://www.khanacademy.org/math/algebra/functions-and-graphs/graphing-functions/a/finding-the-equation-of-a-function-given-its-graph)

Which Equation Represents the Function Graphed on the Coordinate Plane?

Given a graph of a function, it is often possible to determine the equation that represents the function by examining the graph. The following steps can be used to find the equation of a function given its graph:

1. Identify the domain and range of the function. The domain of a function is the set of all values of x for which the function is defined. The range of a function is the set of all values of y that the function can produce.
2. Identify the x-intercepts of the graph. The x-intercepts are the points where the graph crosses the x-axis.
3. Identify the y-intercepts of the graph. The y-intercepts are the points where the graph crosses the y-axis.
4. Identify any asymptotes of the graph. An asymptote is a line that the graph approaches but never touches.
5. Determine the general form of the equation of the function. The general form of the equation of a function is:

“`
y = f(x)
“`

where f(x) is the function of x.
6. Substitute specific values of x into the general equation to find specific values of y. This will allow you to determine the coefficients of the function.
7. Simplify the equation to its most basic form.

Once you have determined the equation of the function, you can use it to make predictions about the function’s behavior. For example, you can use the equation to find the value of y for a given value of x, or you can use the equation to graph the function.

Identify the Domain and Range of the Function

The domain of a function is the set of all values of x for which the function is defined. The range of a function is the set of all values of y that the function can produce.

To identify the domain and range of a function, you can examine the graph of the function. The domain of a function is the set of all x-values that correspond to points on the graph. The range of a function is the set of all y-values that correspond to points on the graph.

In the following example, the domain of the function is all real numbers, and the range of the function is all real numbers greater than or equal to 0.


Identify the x-Intercepts of the Graph

The x-intercepts of a graph are the points where the graph crosses the x-axis. To identify the x-intercepts of a graph, you can look for the points where the graph intersects the x-axis.

In the following example, the x-intercepts of the graph are -2 and 3.


Identify the y-Intercepts of the Graph

The y-intercepts of a graph are the points where the graph crosses the y-axis. To identify the y-intercepts of a graph, you can look for the points where the graph intersects the y-axis.

In the following example, the y-intercept of the graph is 4.


Identify Any Asymptotes of the Graph

An asymptote is a line that the graph approaches but never touches. To identify the asymptotes of a graph, you can look for lines that the graph gets closer and closer to as x approaches infinity or negative infinity.

In the following example, the graph has a horizontal asymptote at y = 0.


Determine the General Form of the Equation of the Function

The general form of the equation of a function is:

“`
y = f(x)
“`

where f(x) is the function of x.

To determine the general form of the equation of a function, you can start by identifying the type of function. There are many different types of functions, but some of the most common types include linear functions, quadratic functions, and exponential functions.

Once you

Q: Which equation represents the function graphed on the coordinate plane?

A: There are a few different ways to find the equation of a function given its graph. One way is to use the slope-intercept form of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope, you can use the following formula:

“`
m = (y2 – y1)/(x2 – x1)
“`

where (x1, y1) and (x2, y2) are two points on the line. Once you have the slope, you can plug it and the y-intercept into the slope-intercept form to find the equation of the line.

Another way to find the equation of a function given its graph is to use the point-slope form of a line, which is y – y1 = m(x – x1), where (x1, y1) is a point on the line and m is the slope of the line. To find the slope, you can use the following formula:

“`
m = (y2 – y1)/(x2 – x1)
“`

where (x1, y1) and (x2, y2) are two points on the line. Once you have the slope, you can plug it and the point (x1, y1) into the point-slope form to find the equation of the line.

Finally, you can also find the equation of a function given its graph by using the following steps:

1. Find the x-intercepts of the function. These are the points where the graph crosses the x-axis.
2. Find the y-intercepts of the function. These are the points where the graph crosses the y-axis.
3. Find the turning points of the function. These are the points where the graph changes direction.
4. Plot the points found in steps 1-3 on a graph.
5. Draw a smooth curve through the points.
6. The equation of the function is the equation of the curve you drew.

Q: What are the different types of functions?

A: There are many different types of functions, but some of the most common include:

• Linear functions: These functions have a constant slope and can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
• Quadratic functions: These functions have a U-shaped graph and can be written in the form y = ax2 + bx + c, where a, b, and c are constants.
• Exponential functions: These functions grow or decay exponentially and can be written in the form y = abx, where a and b are constants.
• Logarithmic functions: These functions are the inverse of exponential functions and can be written in the form y = logx, where x is a positive real number.

Q: How do you find the equation of a function given its graph?

A: There are a few different ways to find the equation of a function given its graph. One way is to use the slope-intercept form of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope, you can use the following formula:

“`
m = (y2 – y1)/(x2 – x1)
“`

where (x1, y1) and (x2, y2) are two points on the line. Once you have the slope, you can plug it and the y-intercept into the slope-intercept form to find the equation of the line.

Another way to find the equation of a function given its graph is to use the point-slope form of a line, which is y – y1 = m(x – x1), where (x1, y1) is a point on the line and m is the slope of the line. To find the slope, you can use the following formula:

“`
m = (y2 – y1)/(x2 – x1)
“`

where (x1, y1) and (x2, y2) are two points on the line. Once you have the slope, you can plug it and the point (x1, y1) into the point-slope form to find the equation of the line.

Finally, you can also find the equation of a function given its graph by using the following steps:

1. Find the x-intercepts of the function. These are the points where the graph crosses the x-

In this blog post, we have discussed the different ways to find the equation of a function graphed on the coordinate plane. We first reviewed the general form of a linear equation, quadratic equation, and exponential equation. Then, we showed how to find the equation of a line using its slope and y-intercept, and how to find the equation of a parabola using its vertex and directrix. Finally, we discussed how to find the equation of an exponential function using its initial value and growth rate. We hope that this blog post has been helpful in understanding how to find the equation of a function graphed on the coordinate plane.