Question

Your friend hands you a graph of the performance statistics of the latest powerboat to be produced. She says, "I know this is a translated graph of either x3 or x4, but I can't figure out which one." Using complete sentences, explain to your friend how to tell if it is an even or odd function, and how to determine the amount the graph has been translated.

Answer 1

I can tell if it is an odd or even function by looking at the degree of the leading coefficient, right?

Answer 2

Other than that, I do not know "how to determine the amount the graph has been translated". Any help? Please?

Answer 3

@phi Is there any way you could help me? I'd really appreciate it!

Answer 4

compare
\[ y = x^3 \]
and
\[ y = x^4\]

when x is very negative... say x= -100, what is y for the first equation
y = -100 * -100 * -100 = -100000
and in general, as x goes more negative, y zooms *down*

on the other hand , for x going more positive, say x=100
y = 100*100*100= 1000000 and y zooms *up*

can you do the same kind of thinking for x^4 ?

Answer 5

Here is a plot of both

Answer 6

a graph can be translated up/down. For y= x^4, the minimum is y=0
if you see a graph that has a minimum of (for example) y=2
you know the graph was shifted up by 2

Answer 7

I'm sorry, I don't understand so far.

Answer 8

Can you explain to me what the question is asking again? They want to know how much the function has been translated? Doesn't that mean they want to know how much it has been shifted? Like from different sets of points?

Answer 9

I hope that makes sense..

Answer 10

Here is x^4. the original, and a shifted version

Answer 11

Is it clear that the black curve is shifted up by 2 steps ?

Answer 12

Yes, I understand. (:

Answer 13

Now if we move it sideways

Answer 14

we moved it 2 steps to the right. The exact amount might be hard to judge...

Answer 15

Okay, that's fine. Why did we move it to the side?

Answer 16

so you can describe how you know it was translated, and by how much.

I would say the point (2,0) in the translated graph corresponds to the point (0,0) in the original graph, so we know the x^4 graph has been translated to the right by 2 steps.

Answer 17

**explain to your friend how to tell if it is an even or odd function,***

if they show only the graph and not the equation, you know it is even if the two "halves" look the same (both zoom up for x^4)
and the graph is x^3 if one graph zooms up on the right and down on the left side.
(see graph up above)

Answer 18

For this graph, is it x^3 or x^4
has it been translated ?

Answer 19

I'm sorry, I don't want to frustrate you, but I guess I just do not understand the problem. I don't want to waste any more of your time. I appreciate everything, but I will see what I can do on my own based on what information you have given me. Thank you so much!

Answer 20

The question asks two things.
First part:
"I know this is a translated graph of either x3 or x4, but I can't figure out which one."

Using complete sentences, explain to your friend how to tell if it is an even or odd function,

Looking at the graph, could you decide if you were looking at x^3 or x^4 ?