Question

To graph the function f(x)= ^3sqrt(x+5)-12 start with the graph f(x)=^3sqrt(x) ..

A. Shift the graph of left by 5 units.
B. Shift the graph of right by 5 units.
C. Shift the graph of up by 5 units.
D. Shift the graph of down by 5 units.
E. Shift the graph of left by 12 units.
F. Shift the graph of right by 12 units.
G. Shift the graph of up by 12 units.
H. Shift the graph of down by 12 units.
I. Reflect the graph of over the x-axis.
J. Reflect the graph of over the y-axis.
K. Stretch the graph of horizontally.
L. Stretch the graph of vertically.

Answer 1

Considering the function \(\normalsize\color{blue}{ f(x)=\sqrt[3]{x} }\)
When you say
\(\normalsize\color{blue}{ f(x)=\sqrt[3]{x+v} }\) you shift it v units left,
and when you say
\(\normalsize\color{blue}{ f(x)=\sqrt[3]{x+v} -c }\) you are not only shifting it v units left, but also c units down.

Answer 2

Thank you very much. In which instances would you reflect and stretch the graph than?

Answer 3

More about the shifts. EXAMPLE.
Looking at, `f(x)=∜x`

f(x)=∜(x `+g`) shift `g` units left
f(x)=∜(x `-g`) shift `g` units right
f(x)=∜(x ) `+g` shift `g` units up
f(x)=∜(x ) `-g` shift `g` units down

Makes sense ?

Answer 4

Also about the `3` that you have before the root. Imagine

y=2│x+1│ and y=6│x+1│ the second one is 3 times skinnier, right?

Answer 5

yes! what about if there is a term out in front? Like g(x)=((1/12)) ^3sqrt(x-6) in relation to ^3sqrtx

Answer 6

3 times skinner? Okay I guess I see how that works!!

Answer 7

Yes, I just said it....
when you take (for the sake of understanding) an absolute value function.
`f(x)=│x│` and `f(x)=3│x│` THEN the `f(x)=3│x│` is going to have a shape of an acute angle opening up, where as `f(x)=│x│` will have a 90º opening up.

And the greater number in front of the absolute value you have, the smaller the degree of the angle opening up is going to be.

Answer 8

Here, we have a similar thing, right ?

Answer 9

oh alright I see

Answer 10

∞ - stands for infinity.

Answer 11

and arrow means 'approaches'

Answer 12

∞ - stands for infinity.

Answer 13

Anyway, back to the simpler level of the prob

Answer 14

Which way do you shift `f(x)=∛x` ? `5` units which direction? And`12` units which direction?
How do you strech the function when you have `f(x) = 3 ∛x` (comparing to JUST `f(x) = ∛x` ?

Answer 15

.

Answer 16

If you need more help, please don't hesitate to say so:)

Answer 17

The one that I just listed for you, so far I have to shift right by 4 units and shift right by 6 units. What am I missing?

Answer 18

Are you looking at the right function, where are you getting numbers 4 and 6 from?

The question was, what is done to `f(x)= ∛x`, to obtain the new function, `f(x)= 3 ∛(x+5)-12`?

Answer 19

No I'll rewrite it

Answer 20

So all this time we are doing the wrong equation ?

Answer 21

No! The first one was right, I'm asking about a different one now haha

Answer 22

Okay, and what is the different function ?

Answer 23

btw, I like cube-root functions, this way you never get imaginary values.