Question

MEDALS GIVEN!!! FAN ADD!!!
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

@skullpatrol @BTaylor @ranga

Answer 2

I just need clarification and possible help on solving step by step?

Answer 3

An odd function is, when you change x to -x, then f(x) will change to -f(x).
That is, f(-x) = -f(x). A cube function, f(x) = x^3 is an odd function. Replace x by -x and f(-x) = (-x)^3 = -(x)^3 = -f(x).

An even function is when you change x to -x, f(x) remains the same.
For example, f(x) = x^2 is an even function. Replace x by -x: f(-x) = (-x)^2 = x^2 = f(x)
f(x) = cos(x) is also an even function.

Even functions will be symmetrical about the y-axis. You can look at a graph and quickly figure out if it is an even function because the right hand side of the graph will be a reflection of the left hand side of the graph about its axis of symmetry.

Answer 4

I should say: Even functions will be symmetrical about their axis of symmetry which will be a vertical line parallel to the y axis or the y axis itself.

Answer 5

So if x=-2 in a function, it will be two spaces left from the y-axis?

Answer 6

by it I mean the x=-2 line of symmetry

Answer 7

Here they are debating if it is a translated graph of x^3 or x^4. x^4 is an even function. It will look something like this: