Problem

Graph each function. See Examples 5 and 6. $$ f…

02:46

Problem 50 Hard Difficulty

Complete each table of function values and then graph each function. See Examples 5 and $6 .$
$$
h(x)=|x+2|
$$
$$
\begin{array}{|r|l|}
\hline \boldsymbol{x} & \boldsymbol{h}(\boldsymbol{x}) \\
\hline-5 & \\
-4 & \\
-3 & \\
-2 & \\
-1 & \\
0 & \\
1 & \\
\hline
\end{array}
$$

Answer

$\begin{array}{|c|l|}\hline x & h(x) \\\hline-5 & 3 \\\hline-4 & 2 \\\hline-3 & 1 \\\hline-2 & 0 \\\hline-1 & 1 \\
\hline 0 & 2 \\\hline 1 & 3 \\\hline\end{array}$

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Algebra

Elementary and Intermediate Algebra

Chapter 3

Graphing Linear Equations and Inequalities in Two Variables; Functions

Section 8

An Introduction to Functions

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Video Transcript

and this problem, we're given the function H of X is equal to the absolute value of X plus two. We're being asked to fill in a tight table, so start when X is negative. Five. That essentially means we want to find a tch of negative five. Well, that simply means we need to substitute negative five in for X in our function. So we'll be left with the absolute value of negative five plus two. Well, negative five plus two is negative. Three In the absolute value, negative three is positive. Three. So when X is negative, five h of X is positive. Three. Now let's do it. X is negative for So that means we need to find a tch of negative four again. That just means we need to substitute negative for in for X so we'll have the absolute value of negative four plus two. Well, negative four plus two is negative to the absolute value of negative, too. Is positive to its when X is negative for age of access to Now we'll go the nexus. Negative three. So we're looking for a tch of negative three. Well, when we substitute negative three and four x We get the absolute value of negative three plus two. Well, negative three plus two is negative one. So we have the absolute value of negative one, which is equal to one. So when excess negative three h of X is equal the positive one. Now let's try what X is negative too. So we're being asked to find agent negative, too. So we're gonna substitute negative two in for X so we'll have the absolute value of negative two plus two. Well, negative two plus two is zero. So we'll have the absolute value of zero, which is equal to zero. So when X is negative to H of X is zero Now let's try when X is negative one. So we're looking for a tch of negative one. Well, that just means we're substituting negative one and four X, so we'll have the absolute value of negative one plus two. Well, negative one plus two is positive one. So we have the absolute value of one which is equal to one. So when X is negative, one h of X is excuse me, a positive one. Now we'll do when X is equal to zero. So We're looking for a job zero. So we're gonna substitute zero in for X, so we'll have the absolute value of zero plus two. Well, zero plus two is equal to two, and the absolute value of two is two. So what X zero h of x is too. And lastly, when X is one. So we're looking for each of one. So when we substitute one in for X, we have the absolute value of one plus two. Well, one plus two is equal to three, and the absolute value of three is three. So what exits One each of X is equal to three. And now we've completed our table. Well, the next part of our directions now asks us to graft this function. So I'm going to go to my second screen here, and I'm gonna fill in the table with the same values we just found. So we had 321012 and three. What we need to keep in mind is that h of X is really equal toe. Why? So all of these values in the second column are really the Y values of our repairs. So, for example, when X is negative. Five and h of X is three. That means the order pair negative. 53 is on the graph. So the same thing for each of the following Rose will have the order pair negative for two. That would impair negative 31 The order pairing. Negative to zero. The order, Karen. Negative 11 Do you want repaired? 02 and he ordered pair 13 So now we simply just need to plot all of these points. So let's start with negative 53 That means we need to go left. Five and up. Three. And that will give us a point on our graph. Never plot negative for two. Which means we go left four and up to negative 31 means go Left. Three and up. One negative to zero. Means go left too. But we're not gonna go up or down. Negative 11 means we go left one and up. One 02 means we don't go left or right. We just simply go up too. And 13 means you go right one. Enough three. And now we can plot our points and graft the equation. And if you know this equation. The graph is in the shape of a V, which makes sense because we were given an absolute value function.

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