The Graph Of $y = F(x$\] Intercepts The $x$-axis At \[$(-7,0)\$\], \[$(-3,0)\$\], And \[$(3,0)\$\].Work Out The Coordinates Of The Points Where The Following Graphs Intercept The $x$-axis.a) $y =

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Introduction

In mathematics, the graph of a function is a visual representation of the relationship between the input and output values of the function. The graph of $y = f(x)$ is a fundamental concept in mathematics, and it is essential to understand how to work with it. In this article, we will discuss the graph of $y = f(x)$ and its intercepts with the $x$-axis.

The Graph of $y = f(x)$

The graph of $y = f(x)$ is a set of points in the Cartesian plane that satisfy the equation $y = f(x)$. The graph is a visual representation of the function, and it can be used to determine the input and output values of the function.

Intercepts with the $x$-axis

The $x$-axis is a horizontal line that passes through the origin of the Cartesian plane. The intercepts of the graph of $y = f(x)$ with the $x$-axis are the points where the graph crosses the $x$-axis. These points are called the $x$-intercepts of the graph.

Given Information

We are given that the graph of $y = f(x)$ intercepts the $x$-axis at the points $(-7,0)$, $(-3,0)$, and $(3,0)$. This means that the graph crosses the $x$-axis at these three points.

Worked Example

To work out the coordinates of the points where the graph of $y = f(x)$ intercepts the $x$-axis, we need to use the given information. We are given that the graph intercepts the $x$-axis at the points $(-7,0)$, $(-3,0)$, and $(3,0)$. This means that the $x$-coordinates of these points are $-7$, $-3$, and $3$, respectively.

Solution

Since the graph intercepts the $x$-axis at the points $(-7,0)$, $(-3,0)$, and $(3,0)$, the $x$-coordinates of these points are $-7$, $-3$, and $3$, respectively. Therefore, the coordinates of the points where the graph of $y = f(x)$ intercepts the $x$-axis are:

• $(-7,0)$
• $(-3,0)$
• $(3,0)$

Conclusion

In this article, we discussed the graph of $y = f(x)$ and its intercepts with the $x$-axis. We were given that the graph intercepts the $x$-axis at the points $(-7,0)$, $(-3,0)$, and $(3,0)$. We used this information to work out the coordinates of the points where the graph of $y = f(x)$ intercepts the $x$-axis.

The Graph of $y = f(x)$ and Its Intercepts with the $y$-axis

Introduction

In the previous section, we discussed the graph of $y = f(x)$ and its intercepts with the $x$-axis. In this section, we will discuss the graph of $y = f(x)$ and its intercepts with the $y$-axis.

The Graph of $y = f(x)$

The graph of $y = f(x)$ is a set of points in the Cartesian plane that satisfy the equation $y = f(x)$. The graph is a visual representation of the function, and it can be used to determine the input and output values of the function.

Intercepts with the $y$-axis

The $y$-axis is a vertical line that passes through the origin of the Cartesian plane. The intercepts of the graph of $y = f(x)$ with the $y$-axis are the points where the graph crosses the $y$-axis. These points are called the $y$-intercepts of the graph.

Given Information

We are given that the graph of $y = f(x)$ intercepts the $y$-axis at the point $(0,5)$. This means that the graph crosses the $y$-axis at this point.

Worked Example

To work out the coordinates of the point where the graph of $y = f(x)$ intercepts the $y$-axis, we need to use the given information. We are given that the graph intercepts the $y$-axis at the point $(0,5)$. This means that the $y$-coordinate of this point is $5$.

Solution

Since the graph intercepts the $y$-axis at the point $(0,5)$, the $y$-coordinate of this point is $5$. Therefore, the coordinates of the point where the graph of $y = f(x)$ intercepts the $y$-axis are:

• $(0,5)$

Conclusion

In this article, we discussed the graph of $y = f(x)$ and its intercepts with the $y$-axis. We were given that the graph intercepts the $y$-axis at the point $(0,5)$. We used this information to work out the coordinates of the point where the graph of $y = f(x)$ intercepts the $y$-axis.

The Graph of $y = f(x)$ and Its Intercepts with the $x$-axis and $y$-axis

Introduction

In the previous sections, we discussed the graph of $y = f(x)$ and its intercepts with the $x$-axis and $y$-axis separately. In this section, we will discuss the graph of $y = f(x)$ and its intercepts with both the $x$-axis and $y$-axis.

The Graph of $y = f(x)$

The graph of $y = f(x)$ is a set of points in the Cartesian plane that satisfy the equation $y = f(x)$. The graph is a visual representation of the function, and it can be used to determine the input and output values of the function.

Intercepts with the $x$-axis and $y$-axis

The intercepts of the graph of $y = f(x)$ with the $x$-axis and $y$-axis are the points where the graph crosses both the $x$-axis and $y$-axis. These points are called the $x$-intercepts and $y$-intercepts of the graph.

Given Information

We are given that the graph of $y = f(x)$ intercepts the $x$-axis at the points $(-7,0)$, $(-3,0)$, and $(3,0)$, and it intercepts the $y$-axis at the point $(0,5)$. This means that the graph crosses both the $x$-axis and $y$-axis at these points.

Worked Example

To work out the coordinates of the points where the graph of $y = f(x)$ intercepts both the $x$-axis and $y$-axis, we need to use the given information. We are given that the graph intercepts the $x$-axis at the points $(-7,0)$, $(-3,0)$, and $(3,0)$, and it intercepts the $y$-axis at the point $(0,5)$. This means that the $x$-coordinates of these points are $-7$, $-3$, and $3$, and the $y$-coordinate of this point is $5$.

Solution

Since the graph intercepts the $x$-axis at the points $(-7,0)$, $(-3,0)$, and $(3,0)$, and it intercepts the $y$-axis at the point $(0,5)$, the coordinates of the points where the graph of $y = f(x)$ intercepts both the $x$-axis and $y$-axis are:

• $(-7,0)$
• $(-3,0)$
• $(3,0)$
• $(0,5)$

Conclusion

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Introduction

In our previous articles, we discussed the graph of $y = f(x)$ and its intercepts with the $x$-axis and $y$-axis. In this article, we will answer some frequently asked questions about the graph of $y = f(x)$ and its intercepts.

Q1: What is the graph of $y = f(x)$?

A1: The graph of $y = f(x)$ is a set of points in the Cartesian plane that satisfy the equation $y = f(x)$. The graph is a visual representation of the function, and it can be used to determine the input and output values of the function.

Q2: What are the intercepts of the graph of $y = f(x)$?

A2: The intercepts of the graph of $y = f(x)$ are the points where the graph crosses the $x$-axis and $y$-axis. These points are called the $x$-intercepts and $y$-intercepts of the graph.

Q3: How do I find the $x$-intercepts of the graph of $y = f(x)$?

A3: To find the $x$-intercepts of the graph of $y = f(x)$, you need to set $y = 0$ in the equation $y = f(x)$ and solve for $x$. This will give you the $x$-coordinates of the points where the graph crosses the $x$-axis.

Q4: How do I find the $y$-intercepts of the graph of $y = f(x)$?

A4: To find the $y$-intercepts of the graph of $y = f(x)$, you need to set $x = 0$ in the equation $y = f(x)$ and solve for $y$. This will give you the $y$-coordinate of the point where the graph crosses the $y$-axis.

Q5: What is the difference between the $x$-intercepts and $y$-intercepts of the graph of $y = f(x)$?

A5: The $x$-intercepts of the graph of $y = f(x)$ are the points where the graph crosses the $x$-axis, and the $y$-intercepts are the points where the graph crosses the $y$-axis. The $x$-intercepts are the points where the graph has an $x$-coordinate of $0$, and the $y$-intercepts are the points where the graph has a $y$-coordinate of $0$.

Q6: How do I graph the function $y = f(x)$?

A6: To graph the function $y = f(x)$, you need to plot the points that satisfy the equation $y = f(x)$ on a Cartesian plane. You can use a graphing calculator or a computer program to help you graph the function.

Q7: What are some common types of functions that have intercepts?

A7: Some common types of functions that have intercepts include linear functions, quadratic functions, and polynomial functions. These functions can have one or more $x$-intercepts and $y$-intercepts, depending on the equation of the function.

Q8: How do I find the equation of a function given its intercepts?

A8: To find the equation of a function given its intercepts, you need to use the $x$-intercepts and $y$-intercepts to determine the equation of the function. You can use the fact that the $x$-intercepts are the points where the graph has an $x$-coordinate of $0$, and the $y$-intercepts are the points where the graph has a $y$-coordinate of $0$.

Conclusion

In this article, we answered some frequently asked questions about the graph of $y = f(x)$ and its intercepts. We discussed the definition of the graph of $y = f(x)$, the intercepts of the graph, and how to find the $x$-intercepts and $y$-intercepts of the graph. We also discussed how to graph the function $y = f(x)$ and how to find the equation of a function given its intercepts.