/*! 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 37 Sketch the graph of the function... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 37

Sketch the graph of the function. $$f(x)=\left\\{\begin{array}{ll}1-(x-1)^{2}, & x \leq 2 \\\\\sqrt{x-2}, & x>2\end{array}\right.$$

Short Answer

Expert verified
The graph of the function will appear as a downward-opening parabola that transitions at \( x = 2 \) into a square root function.

Step by step solution

01

Identify function forms

The function is split into two piece-wise parts which are based on the conditions of \( x \). On observing, we note that the first function for \( x \leq 2 \) is a form of parabola \( 1 - (x-1)^2 \) which opens downwards and the second function for \( x > 2 \) is a form of square root function \( \sqrt{x-2} \) moved 2 units to the right.
02

Sketch function forms

First sketch the parabola \( 1 - (x-1)^2 \) which will have its vertex at \( x = 1 \) and \( y = 1 \). This will be joined by an open circle at \( x = 2 \). Then sketch the square root function \( \sqrt{x-2} \), which begins its domain from \( x = 2 \), with a filled circle at \( x = 2 \), since the endpoint of the first piece-wise function does not include \( x = 2 \), but the second piece-wise function does.
03

Combine the sketches

Final step involves merging or joining the sketches from step 2 into one graph. The final graph will contain a parabola and a square root function, combining at \( x = 2 \), illustrating the function \( f(x) \).Make sure to use open and closed circles to denote inclusive or exclusive endpoints on the piecewise function.

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 Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring. An overhead garage door has two springs, one on each side of the door. A force of 15 pounds is required to stretch each spring 1 foot. Because of a pulley system, the springs stretch only one-half the distance the door travels. The door moves a total of 8 feet, and the springs are at their natural lengths when the door is open. Find the combined lifting force applied to the door by the springs when the door is closed.

Data Analysis: Light Intensity A light probe is located \(x\) centimeters from a light source, and the intensity \(y\) (in microwatts per square centimeter) of the light is measured. The results are shown as ordered pairs \((x, y)\) (Spreadsheet at LarsonPrecalculus,com) $$\begin{array}{lll} (30,0.1881) & (34,0.1543) & (38,0.1172) \\ (42,0.0998) & (46,0.0775) & (50,0.0645) \end{array}$$ A model for the data is \(y=262.76 / x^{2.12}\) A. Use a graphing utility to plot the data points and the model in the same viewing window. B. Use the model to approximate the light intensity 25 centimeters from the light source.

Determine whether the statements use the word function in ways that are mathematically correct. Explain your reasoning. (a) The sales tax on a purchased item is a function of the selling price. (b) Your score on the next algebra exam is a function of the number of hours you study the night before the exam.

Finding a Mathematical Model In Exercises \(41-50\), find a mathematical model for the verbal statement. Newton's Law of Universal Gravitation: The gravitational attraction \(F\) between two objects of masses \(m_{1}\) and \(m_{2}\) is jointly proportional to the masses and inversely proportional to the square of the distance \(r\) between the objects.

Find the difference quotient and simplify your Answer: $$f(x)=x^{2 / 3}+1, \quad \frac{f(x)-f(8)}{x-8}, \quad x \neq 8$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.