# Horizontal Stretching of Functions: What You Need to Know for Common Core Algebra 2 Homework

## Horizontal Stretching of Functions Common Core Algebra 2 Homework

Do you need help with horizontal stretching of functions common core algebra 2 homework? If so, you have come to the right place. In this article, we will explain what horizontal stretching of functions is, how it affects the graphs of different types of functions, and how to apply it to solve some common core algebra 2 homework problems. By the end of this article, you will have a better understanding of this topic and be able to ace your homework assignments.

## horizontal stretching of functions common core algebra 2 homework

## What is Horizontal Stretching of Functions?

A horizontal stretch of a function is a transformation that changes the shape of the function by expanding or compressing it along the x-axis. It is also called a horizontal dilation or a horizontal scaling. A horizontal stretch of a function f(x) by a factor of b is written as g(x) = f(bx), where b is a positive constant. The value of b determines how much the function is stretched or compressed horizontally. If b > 1, then the function is compressed by a factor of b. If 0

Horizontal stretching of functions affects the domain and range of the function, as well as its intercepts, asymptotes, and end behavior. However, it does not affect the y-values or the vertical position of the function.

## How to Graph Horizontal Stretching of Functions?

To graph a horizontal stretch of a function, we can use the following steps:

Identify the original function f(x) and the constant factor b.

Find the new function g(x) = f(bx) by replacing x with bx in f(x).

Plot some points on the graph of f(x) and label their coordinates as (x, f(x)).

Divide each x-coordinate by b to get the corresponding x-coordinate on the graph of g(x). The y-coordinate remains unchanged. Label these points as (x/b, f(x)).

Draw the graph of g(x) by connecting the points (x/b, f(x)).

Alternatively, we can use a graphing calculator to graph both functions and compare them.

## How to Solve Common Core Algebra 2 Homework Problems Involving Horizontal Stretching of Functions?

Here are some examples of common core algebra 2 homework problems that involve horizontal stretching of functions:

Given f(x) = sinx, graph g(x) = f(3x) and find its period and amplitude.

Solution: To graph g(x), we replace x with 3x in f(x):

g(x) = f(3x) = sin3x

We can plot some points on the graph of f(x) and label them as (x, f(x)):

x-pi/2-pi/60pi/6pi/2

f(x)-1-0.500.51

We can divide each x-coordinate by 3 to get the corresponding x-coordinate on the graph of g(x). The y-coordinate remains unchanged. We label these points as (x/3, f(x)):

x/3-pi/6-pi/180pi/18pi/6

f(t)-1-0.500.51

We can draw the graph of g(t) by connecting these points:

The period of g(t) is pi/3, which is one third of the period of f(t). The amplitude of g(t) is 1, which is the same as the amplitude of f(t).

Given f(x) = e^x, graph g(x) = f(0.5x) and find its y-intercept and asymptote.

Solution: To graph g(x), we replace x with 0.5x in f(x):

g(x) = f(0.5x) = e^(0.5x)

We can plot some points on the graph of f(x) and label them as (x, f(x)):

x-2-1012

f(t)e^-2e^-1e^0e^1e^2

We can multiply each x-coordinate by 2 to get the corresponding x-coordinate on the graph of g(t). The y-coordinate remains unchanged. We label these points as (2x, f(t)):

x/4-4-2024

f(t)e^-2e^-1e^0e^1e^2

We can draw the graph of g(t) by connecting these points:

The y-intercept of g(t) is (0, e^0), which is (0, 1). The asymptote of g(t) is y = 0.

Given f(x) = lnx, graph h(x) = f(4x - 8) + 3 and find its domain and range.

Solution: To graph h(x), we replace x with 4x - 8 in f(x) and add 3:

h(x) = f(4x - 8) + 3 = ln4x - 8 + 3

We can plot some points on the graph of f(x) and label them as (x, f(x)):

xe^-1+8/4e^0+8/4e^1+8/4

f(t)-1+30+31+3

We can divide each x-coordinate by 4 and subtract 8 to get the corresponding x-coordinate on the graph of h(t). We subtract 3 from each y-coordinate to get the corresponding y-coordinate on the graph of h(t). We label these points as ((x - 8)/4, f(t) - 3):

(t-8)/4e^-1+8-8/4-3e^0+8-8/4-3e^1+8-8/4-3

f(t)-3-1-3

We can draw the graph of h(t) by connecting these points:

The domain of h(t) is (2, infinity). The range of h(t) is (-infinity, infinity).

## Why is Horizontal Stretching of Functions Important?

Horizontal stretching of functions is an important topic in common core algebra 2 because it helps us understand how different functions behave and how they can be transformed to model different situations. For example, horizontal stretching of functions can be used to:

Compare the growth rates of different exponential functions.

Analyze the effects of frequency on periodic functions such as sine and cosine.

Modify the shape and width of probability distributions such as normal and logistic.

Create new functions from existing ones by combining horizontal stretching with other transformations such as shifting, reflecting, and vertical stretching.

Horizontal stretching of functions also helps us develop our algebraic skills and our graphical intuition. By learning how to manipulate functions algebraically and graphically, we can solve more complex problems and explore more advanced concepts in mathematics.

## How to Practice Horizontal Stretching of Functions Common Core Algebra 2 Homework?

If you want to practice horizontal stretching of functions common core algebra 2 homework, you can use various resources such as textbooks, worksheets, online videos, and interactive tools. Here are some tips to help you practice effectively:

Review the definitions and properties of horizontal stretching of functions and how they apply to different types of functions such as linear, quadratic, exponential, logarithmic, trigonometric, and rational.

Practice graphing horizontal stretches of functions by hand and by using a graphing calculator. Compare the graphs of the original function and the stretched function and identify how they are related.

Practice solving problems that involve horizontal stretching of functions by applying the appropriate formulas and techniques. Check your answers by plugging them back into the original equation or by using a graphing calculator.

Practice creating your own problems that involve horizontal stretching of functions by choosing a function and a constant factor and writing an equation for the stretched function. Then graph both functions and verify that they are horizontally stretched.

By practicing horizontal stretching of functions common core algebra 2 homework regularly, you will improve your understanding of this topic and be prepared for your tests and exams.

## Conclusion

In this article, we have explained what horizontal stretching of functions is, how to graph it, and how to solve some common core algebra 2 homework problems involving it. We have also discussed why horizontal stretching of functions is important and how to practice it effectively. We hope that this article has helped you learn more about this topic and that you will enjoy exploring it further.

## Horizontal Stretching of Functions Common Core Algebra 2 Homework Tips and Tricks

Now that you have learned how to graph and solve horizontal stretching of functions common core algebra 2 homework problems, here are some tips and tricks to help you master this topic and avoid common mistakes:

Remember that horizontal stretching of functions is the opposite of horizontal compression of functions. To horizontally stretch a function by a factor of b, you need to multiply the input value by b. To horizontally compress a function by a factor of b, you need to divide the input value by b.

Remember that horizontal stretching of functions does not affect the y-values or the vertical position of the function. It only affects the x-values and the horizontal position of the function.

Remember that horizontal stretching of functions changes the domain and range of the function, as well as its intercepts, asymptotes, and end behavior. To find these values, you need to apply the inverse operation of horizontal stretching to the original function.

Remember that horizontal stretching of functions can be combined with other transformations such as shifting, reflecting, and vertical stretching. To graph these composite transformations, you need to apply them in the correct order and follow the rules for each transformation.

Remember that horizontal stretching of functions can be applied to different types of functions such as linear, quadratic, exponential, logarithmic, trigonometric, and rational. To graph these functions, you need to know their basic shapes and properties and how they are affected by horizontal stretching.

By following these tips and tricks, you will be able to graph and solve horizontal stretching of functions common core algebra 2 homework problems with ease and confidence.

## Horizontal Stretching of Functions Common Core Algebra 2 Homework Resources

If you want to learn more about horizontal stretching of functions common core algebra 2 homework or practice your skills further, you can use various resources such as textbooks, worksheets, online videos, and interactive tools. Here are some examples of resources that you can use:

Unit 7 - Transformations of Functions - eMATHinstruction: This website provides lessons, videos, worksheets, answer keys, assessments, and add-ons for common core algebra 2 topics including horizontal stretching of functions.

Common Core Algebra I.Unit #11.Lesson #2.Horizontal Stretching of Functions: This video explains how to recognize the effects of horizontal stretches and compressions on a function's graph using examples and graphs.

Free Solutions for Algebra 2 Common Core Quizlet: This website provides step-by-step solutions and answers to algebra 2 common core textbook problems including horizontal stretching of functions.

Desmos Graphing Calculator: This website provides an online graphing calculator that allows you to graph any function and apply transformations such as horizontal stretching.

By using these resources, you will be able to enhance your learning and practice your skills on horizontal stretching of functions common core algebra 2 homework.

## Conclusion

In this article, we have covered everything you need to know about horizontal stretching of functions common core algebra 2 homework. We have explained what horizontal stretching of functions is, how to graph it, and how to solve some common core algebra 2 homework problems involving it. We have also discussed why horizontal stretching of functions is important and how to practice it effectively. We have also provided some tips and tricks to help you master this topic and avoid common mistakes. Finally, we have shared some resources that you can use to learn more and practice your skills on horizontal stretching of functions common core algebra 2 homework.

We hope that this article has helped you understand and enjoy this topic and that you will be able to ace your homework assignments and tests on horizontal stretching of functions common core algebra 2 homework. Thank you for reading and happy learning! 4e3182286b