Translations Homework Problem: shifting 3x^3 - 2x^2 + 8x - 12

foxqood

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I'm doing pretty good on my translations homework, but there's one problem that I can't figure out for the life of me!

Here's the problem: Shift 3x^3-2x^2+8x-12 right 4 units, down 3 units, and reflect across the x-axis. Write the new equation in its simplest form.


So far, the only step I've been able to take is to move the equation down three units; it looks like 3x^3-2x^2+8x-15 after that step is taken.

I'm brand new after finally acknowledging the fact that I might need help, and I don't know how to insert an image of what this looks like on a graph.

I know that to shift the equation right four units, I have to apply to all of the x's, but I'm not 100% sure how to do that to squares or cubes.


Thank you so much to anybody who is able to help!! :grin::)
 
You actually seem like you have the idea.

How would you shift y = x - 3 four units to the right? (no squares or cubes)
 
I'm doing pretty good on my translations homework, but there's one problem that I can't figure out for the life of me!

Here's the problem: Shift 3x^3-2x^2+8x-12 right 4 units, down 3 units, and reflect across the x-axis. Write the new equation in its simplest form.

So far, the only step I've been able to take is to move the equation down three units; it looks like 3x^3-2x^2+8x-15 after that step is taken.

I'm brand new after finally acknowledging the fact that I might need help, and I don't know how to insert an image of what this looks like on a graph.

I know that to shift the equation right four units, I have to apply to all of the x's, but I'm not 100% sure how to do that to squares or cubes.

Thank you so much to anybody who is able to help!! :grin::)

First, a terminology issue: what you show isn't an equation at all, but an expression. I suppose you were instructed to shift and reflect the equation y = 3x^3-2x^2+8x-12.

A horizontal shift (right c units) is accomplished by replacing x with x-c throughout. For example, 3x^3 becomes 3(x-c)^3.
 
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