/*! 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 31 Graph each equation in Exercises... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 31

Graph each equation in Exercises 21-32. Select integers for \(x\) from \(-3\) to 3 , inclusive. \(y=|x|+1\)

Short Answer

Expert verified
The graph is a V-shaped line, symmetric about the y-axis and shifted upward by 1.

Step by step solution

01

Understanding Absolute Value

An absolute value of a number is its distance from zero, always a non-negative value. For this equation \(y = |x| + 1\), which is a shifted version of the basic absolute value function \(y = |x|\), where the shift is up by 1.
02

Calculate y-values

Now, for each integral value of \(x\) in the range -3 to 3, calculate the corresponding \(y\)-values using the equation, which means taking the absolute value of \(x\) and adding 1 to it.
03

Graphing the Point

Plot all the points that have been computed and connect these points with two straight lines. This will construct the graph of \(y = |x| + 1\).
04

Verify

The graph should be V-shaped and symmetric about the y-axis because absolute value function always yields a symmetric, V-shaped graph.

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