graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting:?

Question

f(x) = |x - 2|- 3

What are the steps for this problem and is there a program i can use to graph this out?

Answer 1

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Remeber:

f(x) = Function

shifting:

f(x+c) = c units to the left

f(x-c) = c units to the right

f(x)+c = c units up

f(x)-c = c units down

Scales:

f(x)/c = compressing c units vertically

cf(x) = stretching c units vertically

f(x/c) = stretching c units horizontally

f(cx) = compressing c units horizontally

From the given function, you can easily see that the basic function is f(x)=|x|. We know it's graphic is the following:

fooplot.com/abs(x)

Absolute value of x is defined as: f(x) = |x| = -x if x<0 or x if x>=0, so it may be considered a reflection*

Now, check the given function and compare it with the basic one.

The first you have to do is shifting it 2 units to the right. Mathematically, it means: f(x-2), wich is |x-2|. You'll have this:

fooplot.com/abs(x-2)

Then, move the graph 3 units down. Mathematically, it means: f(x-2)-3, wich is |x-2|-3. And, You got what you wanted:

fooplot.com/abs(x-2)-3

Source(s): Sorry nobody responded on time. I guess you created that account just to ask this. I suppose you waited for about one or two hours, and then realized that "nobody" was going to answer, I know how it feels. Anyways, I hope to be wrong. At least someone may get here later and find this usefull. Luck. Reader, excuse me for my english, I know it sucks : | Graphinc website: fooplot.com/