/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 47 Use transformations of \(f(x)=\f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 47

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{x}+2$$

Short Answer

Expert verified
The graph of the function \(h(x) = \frac{1}{x} + 2\) can be obtained by shifting the graph of the function \(f(x) = \frac{1}{x}\) upward by 2 units.

Step by step solution

01

Identify the base function and transformations

The base function here is \(f(x) = \frac{1}{x}\). The new function \(h(x) = \frac{1}{x} + 2\) is a transformation of the ase function. This is a vertical shift upwards by 2 units.
02

Plot the base function

Begin by plotting the base function \(f(x) = \frac{1}{x}\). This is a hyperbolic function that approaches both the x-axis (asymptote) as \(x\) goes to infinity and negative infinity and approaches the y-axis as \(x\) approaches 0 from both positive and negative directions.
03

Apply the Transformation

To obtain the graph of \(h(x)\), shift the graph of \(f(x)\) upward by 2 units. This means each y-value from the graph of \(f(x)\) is increased by 2 in the graph of \(h(x)\). The asymptote of this function will now be \(y=2\) instead of \(y=0\) because of the upward shift.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use everyday language to describe the behavior of a graph near its vertical asymptote if \(f(x) \rightarrow \infty\) as \(x \rightarrow-2^{-}\) and \(f(x) \rightarrow-\infty\) as \(x \rightarrow-2^{+}\).

Find the inverse of \(f(x)=x^{3}+2\)

Use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$(x-2)^{2}>0$$

If you are given the equation of a rational function, explain how to find the horizontal asymptote, if there is one, of the function's graph.

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g.\) $$g(x)=\frac{3 x-7}{x-2}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.