Problem

Complete each table of function values and then g…

03:03

Problem 47 Hard Difficulty

Complete each table of function values and then graph each function. See Examples 5 and 6.
$$
\begin{aligned}
&f(x)=-3 x-2\\
&\begin{array}{|c|c|}
\hline x & {f(x)} \\
\hline-2 & {} \\
{-1} & {} \\
{0} & {} \\
{1} & {} \\
\hline
\end{array}
\end{aligned}
$$

Answer

$\begin{array}{|r|r|}\hline x & f(x) \\\hline-2 & 4 \\\hline-1 & 1 \\\hline 0 & -2 \\\hline 1 & -5 \\\hline\end{array}$

Related Courses

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

this problem. We're given the function F of X is equal to negative three X minus two were first being asked to find the following function values in the table. So we're trying to find out from negative to effort, negative 1/2 of zero and everyone. So let's start with f of negative two. Or remember the fine effort negative too. We simply need to substitute negative to infer, accent or function so well, have negative three times negative to minus two and now we evaluate. Well, negative three minus two is positive. Six and six minus two is four. So we found when X is negative too. F of X is for we're gonna do the same thing for f of negative one. We're gonna substitute negative one in for X. So we'll have negative three times Negative. One minus two. Well, negative. Three times negative. One is positive. Three and three minus two is equal to one. So when X is negative, one f of X is one. Now we're in the Judas for zero. We're simply going to substitute zero in for X. So have negative. Three times zero minus two. Well, negative. Three times zero is zero and zero minus two is negative too. So when x zero f of X is negative too, and lastly will find off of one by substituting one in for X. So we'll have a negative three times one minus two. Well, negative. Three times one is negative. Three and negative three minus two is equal to negative five. So when X is one f of X is negative. Five. Everything. I want you to know this is the pattern for our table. If you know this ex, each time goes up by one. And our why values go down by three each time and know this in your equation for our slope, it would be negative. Three. That does have a correlation there. Well, the next part of our directions says we now want to graft this equation. So I'm going to go over to the next screen and I'm gonna fill in the values that we already found. So we have four one negative too, and negative five will remember the F of X needs the same thing as why so essentially these values in the second column are, Why values? So when we're going to plot these points in that first row when X is negative. Two in f of X is for that really corresponds to the point negative to four. So our second row corresponds to the point. Negative 11 The third row would be zero negative too. And the fourth row would be one negative five. And now we simply need the plot. These points well to plot the point negative to four. We go left to and up for the plot to point negative 11 We go left one and up. One The plot. The 0.0 negative too. We don't go left or right. We just go down to and to plot the 0.1 negative five We go right one and down five and now we can connect these points. I'm going to do the best I can to make this a straight. It's possible. I know him off by a little bit. That's just due to me writing this on my own. And now with graft, the equation

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