2. (6 pts.) The graph of the function y = f(x) is shown...

2. (6 pts.) The graph of the function y = f(x) is shown below. Use it to graph each of the following functions. (a) g(x) = -1/2 f(x+1) (b) h(x) = f(2x+8) 3. (5 pts.) Find an equation of the function f(x) graphed below. Show your work: start with the basic function, then describe transformations, and finally write an equation.

Transcript

00:01 Use the given graph to graph each of the following functions.

00:03 Let's start with g of x.

00:05 What you need to notice here is we have this expression which changes our x values.

00:10 So we have our ordered pairs here.

00:12 I've listed.

00:13 Let me go ahead and put them here.

00:15 Negative 2, negative 2, 0, negative 1, 1, and 3, 4.

00:23 We change our x values in the manner.

00:25 We say x plus 1, x plus 1 equals negative 2.

00:33 So therefore x equals to negative 3.

00:39 X plus 1 equals 0, therefore x equals negative 1.

00:45 X plus 1 equals 1, therefore x equals 0.

00:49 X plus 1 equals 3, therefore x equals to 2.

00:55 So in our new ordered pairs, we're going to have x negative 3, negative 1, 0, and 2 for our x values.

01:03 Now the 1 1 .5 is changing our y values.

01:07 We're going to take each of the y values and multiply them by 1 .5.

01:13 So we're going to take 2, negative 2 times 1⁄2, which would be negative 1.

01:20 We're going to take negative 1 times 1⁄2, which will be negative 1⁄2.

01:25 We're going to take 0 times 1⁄2, which will be 0.

01:30 We're going to take 4 times 1⁄2.

01:33 I'm sorry that's negative one half let me change my signs there i just realized i wrote it wrong so i'll be negative 2 so now i have the points of my new for my new graph let's get that here so let me put a few more tick marks in here to make sure that we're all in the same place so i'm going to go negative 3 positive 1 i'm going to go negative 1 1 1 1 half i'm going to go 0 0 and then i'm going to go to negative 2.

02:07 So we're going to draw this graph in the opposite direction as such.

02:15 Now we're going to do the same thing for h of x...

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