The Point { (-3,-5)$}$ Is On The Graph Of A Function. Which Equation Must Be True Regarding The Function?A. { F(-3) = -5$}$B. { F(-3,-5) = -8$}$C. { F(-5) = -3$}$D. { F(-5,-3) = -2$}$

Mar 8, 2025 by ADMIN 184 views

**The Point on the Graph of a Function: Understanding the Equation**

Introduction

In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. When a point is on the graph of a function, it means that the input value of the point corresponds to the output value of the function. In this article, we will explore the concept of a point on the graph of a function and determine which equation must be true regarding the function.

Understanding the Graph of a Function

A graph of a function is a visual representation of the function, where the input values are plotted on the x-axis and the output values are plotted on the y-axis. Each point on the graph represents a pair of input and output values, where the input value is the x-coordinate and the output value is the y-coordinate.

The Point on the Graph

The point ${$ (-3,-5)$}$ is on the graph of a function. This means that the input value of the point is -3 and the output value of the function is -5.

Analyzing the Options

Let's analyze the options given:

A. ${$ f(-3) = -5$}$

This option states that the output value of the function when the input value is -3 is -5. Since the point ${$ (-3,-5)$}$ is on the graph of the function, this option must be true.

B. ${$ f(-3,-5) = -8$}$

This option is incorrect because the input value of the function is -3, not -3,-5. The point ${$ (-3,-5)$}$ is on the graph of the function, but the input value is only -3.

C. ${$ f(-5) = -3$}$

This option is incorrect because the output value of the function when the input value is -5 is not -3. The point ${$ (-3,-5)$}$ is on the graph of the function, but the input value is -3, not -5.

D. ${$ f(-5,-3) = -2$}$

This option is incorrect because the input value of the function is -5,-3, not -3. The point ${$ (-3,-5)$}$ is on the graph of the function, but the input value is only -3.

Conclusion

In conclusion, the equation that must be true regarding the function is:

A. ${$ f(-3) = -5$}$

This equation states that the output value of the function when the input value is -3 is -5. Since the point ${$ (-3,-5)$}$ is on the graph of the function, this equation must be true.

Key Takeaways

A function is a relation between a set of inputs and a set of possible outputs.
A graph of a function is a visual representation of the function.
Each point on the graph represents a pair of input and output values.
The input value of a point on the graph corresponds to the output value of the function.
The equation ${$ f(-3) = -5$}$ must be true regarding the function when the point ${$ (-3,-5)$}$ is on the graph of the function.

Frequently Asked Questions

Q: What is a function? A: A function is a relation between a set of inputs and a set of possible outputs.

Q: What is a graph of a function? A: A graph of a function is a visual representation of the function.

Q: What does a point on the graph of a function represent? A: A point on the graph of a function represents a pair of input and output values.

Q: What is the equation that must be true regarding the function when the point ${$ (-3,-5)$}$ is on the graph of the function? A: The equation that must be true regarding the function is ${$ f(-3) = -5$}$.

References

[1] Khan Academy. (n.d.). Functions. Retrieved from https://www.khanacademy.org/math/algebra-functions
[2] Math Open Reference. (n.d.). Functions. Retrieved from https://www.mathopenref.com/functions.html

Glossary

Function: A relation between a set of inputs and a set of possible outputs.
Graph of a function: A visual representation of the function.
Input value: The x-coordinate of a point on the graph of a function.
Output value: The y-coordinate of a point on the graph of a function.
Q&A: Understanding Functions and Graphs =============================================

Introduction

In our previous article, we explored the concept of a point on the graph of a function and determined which equation must be true regarding the function. In this article, we will answer some frequently asked questions about functions and graphs.

Q&A

Q: What is a function?

A: A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is a way of describing a relationship between two variables, where each input value corresponds to a unique output value.

Q: What is a graph of a function?

A: A graph of a function is a visual representation of the function, where the input values are plotted on the x-axis and the output values are plotted on the y-axis. Each point on the graph represents a pair of input and output values.

Q: What does a point on the graph of a function represent?

A: A point on the graph of a function represents a pair of input and output values. The x-coordinate of the point represents the input value, and the y-coordinate represents the output value.

Q: How do I determine if a point is on the graph of a function?

A: To determine if a point is on the graph of a function, you need to check if the input value of the point corresponds to the output value of the function. If the input value is x and the output value is y, then the point (x, y) is on the graph of the function.

Q: What is the difference between a function and a relation?

A: A function is a relation where each input value corresponds to a unique output value. A relation, on the other hand, is a set of ordered pairs where each input value may correspond to multiple output values.

Q: How do I graph a function?

A: To graph a function, you need to plot the input values on the x-axis and the output values on the y-axis. You can use a table of values or a graphing calculator to help you graph the function.

Q: What is the equation of a function?

A: The equation of a function is a mathematical expression that describes the relationship between the input and output values. It is usually written in the form f(x) = y, where f(x) is the output value and x is the input value.

Q: How do I determine the domain and range of a function?

A: To determine the domain and range of a function, you need to identify the set of input values and the set of output values that the function can take. The domain is the set of input values, and the range is the set of output values.

Q: What is the difference between a linear function and a non-linear function?

A: A linear function is a function that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. A non-linear function is a function that cannot be written in this form.

Q: How do I determine if a function is increasing or decreasing?

A: To determine if a function is increasing or decreasing, you need to check the slope of the function. If the slope is positive, the function is increasing. If the slope is negative, the function is decreasing.