Tip:
Highlight text to annotate it
X
okay, so were're going to start with problem 12 of section 2.2
essentially what we're going to do is graph this piece wise function that you can see in the upper right hand corner of the screen
so give me a second while I write that down
Essentially what this is, is the absolute value function
so what we're going to be doing for the piece wise function is graphing two different lines.
we're going to graph this line when x is less than 0.
and we're going to graph this line when x is greater than or equal to 0.
So let's start out by drawing a number line
and over here I'm going to make a table
So first we're going to do case number 1
and I'm going to put values for x
now remember that for this case we need to choose values that are less than 0.
so we're going to pick x = 1
or x= -1 I mean, I'm sorry
Because remember that case 1 is less x<0
Because remember that case 1 is less x<0
Because remember that case 1 is less x<0
so f(-1) = -2(-1) = 2
and I can pick -2 as a value since case I is x<0
and this is going to give me if I plug it into my function
which gives me f(-2) = -2(-2) = 4
so if I plot over here where x=-1
then y=1 so I have this point over here
it's the point negative one two or (-1,2)
and then I have the point minus two, four
which is going to be this point right over here
now this is going to be a straight line since -2x is a straight line
a straight line is anything that can be written in the form y=mx+b
we case 1 can be written in the form y= -2x+0
so in this case m is negative two and b is zero
we can also think of a straight line where x is not raised to any power.
it's not an x squared, or an x cubed, etc
so to graph a straight line you can just plot two points and then connect the two points with a straight line.
so in this case it's going to look like this
we can just extend it
the reason I extend it to zero is because the line for case I only goes to 0
we can start as far to the left as we want but we can only go as far to the right as zero
now for the other case which is case II and I'll do that over here
so we're going to have x and f(x) again
but we're going to pick values that are greater than or equal to zero
So I'm going to pick zero for my first value
and here I'm using this function definition
so it's going to be 2 times whatever number I choose
so if I choose 0 then I have 2 times 0 is 0
and that's my first point
and the I can have x=1. and from my function definition I have 2 times 1 is 2
so my next point is that when x =1, then f(x)=2
so it's going to be like this
so I can connect this points for the same reason, it's just an x, it's not an x squared or anything
so I just connect this point and this point
so that's my graph, and what I'm going to do now is go back and look at the problem
and as you can see answer choice D is the only answer choice that remotely resembles what I graphed
So I'm going to check my answer and it's fantastic
okay so that's all I have, so I hope I answered the question and good luck with week two. Thanks