Graph Compressions

Question

If g(x) is the f(x) =x after a verticle compression, a shift right by 4, and a shift up by 2

write an equation for g(x): g(x)

The slope of this line is:

The vertical intercept of this line is:

Answer 1

Let's tackle each transformation one at a time.

vertical compression

I'm assuming that by vertical compression, you mean squishing the graph so that it's "flatter". We can vertically compress a graph by multiplying the whole function by a fraction less than 1. So if we want to vertically compress the function f(x) by a factor of 2, we would do:

g(x) = 1/2 * f(x)

You didn't say how much you want to vertically compress f(x), so I'm going to use 1/2 as an example for the factor of compression. If you want it more compressed, then multiply f(x) by a smaller number. If you want it less compressed, multiply f(x) by a larger number.

shift right by 4

To shift f(x) right by 4, we decrease x by 4. In other words, if g(x) is the same as f(x), but shifted right 4 units, then:

g(x) = f(x-4)

This makes sense, because we're moving the graph along the x axis. So we change the x value in the function. Remember, subtracting shifts to the right and adding shifts to the left. We want a shift right, which is why we subtracted instead of added.

shift up by 2

To shift f(x) up by 2, we add 2 to the whole function. In other words, if g(x) is the same as f(x), but shifted up 2 units, then

g(x) = f(x) + 2

Notice that we added the 2 outside of the function. That's because we're shifting the graph along the y axis, so we add to the y value ( f(x) generally represents the y value of the function).

Now that we know how to do each transformation individually, we just put them together!

g(x) = 1/2 * f(x-4) + 2

Hope this helped :)