Lesson 4 Homework Practice: Multiple Representations of Functions

In this lesson, you will learn how to represent functions in different ways, such as equations, tables, graphs, and words. A function is a relationship that pairs each input with exactly one output. For example, the function f(x) = 2x + 3 pairs each input x with an output f(x) by multiplying the input by 2 and adding 3.

One way to represent a function is by using an equation. An equation shows how the input and output are related by using symbols and operations. For example, the equation y = 2x + 3 represents the function f(x) = 2x + 3 by using y as the output and x as the input.

Another way to represent a function is by using a table. A table shows the input and output values in rows and columns. For example, the table below shows some input and output values for the function f(x) = 2x + 3.

A third way to represent a function is by using a graph. A graph shows the input and output values as points on a coordinate plane. For example, the graph below shows some input and output values for the function f(x) = 2x + 3.

A fourth way to represent a function is by using words. Words describe how the input and output are related in a sentence or a phrase. For example, the words “the output is two more than twice the input” represent the function f(x) = 2x + 3 by using words.

These are some examples of multiple representations of functions. You can use any of these representations to show or analyze a function. In this lesson, you will practice using multiple representations of functions in different situations.

One of the benefits of using multiple representations of functions is that you can compare and contrast different functions. For example, you can use graphs to see how different functions have different shapes, slopes, and intercepts. You can also use tables to see how different functions have different rates of change and patterns. You can also use equations to see how different functions have different expressions and coefficients.

Another benefit of using multiple representations of functions is that you can use one representation to find another representation. For example, you can use an equation to make a table by plugging in different input values and finding the output values. You can also use a table to make a graph by plotting the input and output values as points on a coordinate plane. You can also use a graph to make an equation by finding the slope and the y-intercept of the line.

A third benefit of using multiple representations of functions is that you can use them to solve real-world problems. For example, you can use an equation to model a situation that involves a constant rate of change, such as the cost of renting a car or the distance traveled by a train. You can also use a table to organize data that shows a relationship between two quantities, such as the number of hours worked and the amount earned. You can also use a graph to visualize a situation that involves a variable rate of change, such as the height of a ball thrown in the air or the population growth of a city.

In this lesson, you have learned how to use multiple representations of functions, such as equations, tables, graphs, and words. You have also learned how to compare and contrast different functions, how to find one representation from another representation, and how to use multiple representations of functions to solve real-world problems.

Now it is time to practice what you have learned. For your homework, you will complete some exercises that involve multiple representations of functions. You will use equations, tables, graphs, and words to represent and analyze different functions. You will also apply your skills to some word problems that require you to use multiple representations of functions.

Remember to check your work and show your steps. If you need help, you can review the examples and explanations in this lesson. You can also ask your teacher or a classmate for assistance. Good luck and have fun!

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