/*! 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 21 Sketch one full period of the gr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 21

Sketch one full period of the graph of each function. $$y=3 \tan x$$

Short Answer

Expert verified
The tangent function has an amplitude of 3, period of \(\pi\), with intercept at x=0, and asymptotes at \(x=-\frac{\pi}{2}\) and \(x=\frac{\pi}{2}\).

Step by step solution

01

Identify the amplitude

The amplitude of the function \(y=3\tan x\) is the coefficient in front of the tangent function, which is 3. This indicates that the function will rise and fall with a rate of 3 units per interval.
02

Identify the period

Since there's no coefficient in front of x, the period of this function is \(\frac{\pi}{1}=\pi\). This means the function will complete a full cycle of its pattern every \(\pi\) units.
03

Identify the critical points

The critical points of the tangent function are its intercepts and asymptotes. For this function, the intercept is at x=0, and the asymptotes occur at \(x=-\frac{\pi}{2}\) and \(x=\frac{\pi}{2}\).
04

Sketch the graph

Plot the intercept and asymptotes identified in step 3 on the graph. These form the skeleton of the graph. Then, sketch the curve between these points. The tangent function rises from negative infinity to positive infinity as x moves from the negative asymptote to the positive asymptote.

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

Estimate, to the nearest tenth, \(\sin \frac{3 \pi}{4}\).

Estimate, to the nearest tenth, \(\cos \frac{5 \pi}{4}\).

Graph at least one full period of the function defined by each equation. $$y=\left|\frac{1}{2} \sin 3 x\right|$$

Graph at least one full period of the function defined by each equation. $$y=-|3 \cos \pi x|$$

Graph at least one full period of the function defined by each equation. $$y=3 \cos \frac{3 \pi x}{2}$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

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.