Question

I got a question wrong about graphing. Can someone explain to me what I did wrong, and how to find the right answer in as much detail as possible? I really appreciate the help.

Answer 1

ok first thing that might be really helpful when graphing is checking if the function is odd or even or not even and not odd

do you know what are even\odd functions ?

Answer 2

yes.. in this case what kind of function is it ?

Answer 3

correct

Answer 4

in this case we have
f(-x) = (-x)^(1/3) = (-1)^(1/3) * x^(1/3) = -(x^(1/3))

Answer 5

it is odd.. so odd function means symmetry about the origin
you can see that this graph is symmetric about the origin

Answer 6

now next thing you should do is looking for points on x^(1/3) and see if it's agree with the graph

0^(1/3) =0 like the graph
(1)^(1/3) = 1 like the graph
(-1)^(1/3) = -1 like the graph

no you see that we dont have any other "exact" point
but if you know that 2^3 = 8
so you know that 8^(1/3) = 2
it looks about right on this graph (even though you dont see 8 it looks like its going to be)

Answer 7

yes

Answer 8

yes\[f(-x) = (-x)^{1/3} = (-1)^{1/3} * (x)^{1/3} = -1 * (x)^{1/3} = - \sqrt[3]{x} = -f(x)\]

Answer 9

tell me if you understand the other thing i said about finding points on the graph and if it fits the equation

Answer 10

in fact there are more to do in order to graph.. you have to take derivatives and find maximum\minimum points and Inflection points but in here you dont really have to do all this work

Answer 11

if you feel that it is good enough so yes
in this case since you had a graph the easiest thing to do is checking for points
when you dont have a graph and you have a complicated function you have to do more work

Answer 12

ok ill be there lol