Question

y=x³+4

Answer 1

You would probably like to know that you can put up ¹ , ² , ³ just using the keyboard.

1) Click and hold ALT
2) click the number code (using the numbers that are on the right of the keyboard, not the ones below F1, F2, F3, etc., ) 3) release the ALT

If you click `0 1 8 5` you get, ¹
If you click `2 5 3` you get, ²
If you click `0 1 7 9` you get, ³

(There are more different ALT-CODES for various symbols.)

Anyway, now back to your problem
••••

You are probably asked to graph this function, so I would be plugging in random numbers for x (just the same way as graphing a line).

\(\normalsize\color{black}{ y=x^3+4 }\)

When `x=0` ,
y=x³+4
y=(0)³+4
y=0+4
y=4
THUS, we get (0,4).

When `x=1` ,
y=x³+4
y=(1)³+4
y=1+4
y=5
THUS, we get (1,5).

When `x=2` ,
y=x³+4
y=(2)³+4
y=8+4
y=12
THUS, we get (1,5).

When `x=1` ,
y=x³+4
y=(1)³+4
y=1+4
y=5
THUS, we get (1,5).

Now lets plug in some negative values ....

When `x=-1` ,
y=x³+4
y=(-1)³+4
y=-1+4
y=3
THUS, we get (-1,3).

When `x=-1` ,
y=x³+4
y=(-1)³+4
y=-1+4
y=3
THUS, we get (-1,3).

When `x=-2` ,
y=x³+4
y=(-2)³+4
y=-8+4
y=-4
THUS, we get (-2,-4).

And so on.... you see what am doing here, right?

I'll show you what it will look like, https://www.desmos.com/calculator/buywhyvvjn

You can see though that `y=x³+4` is the same as `y=x³`, but shifted 4 units up.
Here, I'll show you this,
https://www.desmos.com/calculator/elpbdsr9mx
(the blue curve is `y=x³+4`, AND the black curve is `y=x³`)

The rules for the function shifts are as follows,

\(\large\color{ blue }{\large {\bbox[5pt, yellow ,border:2px solid white ]{ \large\text{ }\\
\begin{array}{|c|c|c|c|}
\hline~~~~~~~~~~~~~~~~~~~~~~~~~~~\textbf{Shifts}~~~~~~~~~~~~~~~~~~~~~~~~~~~&~\rm{c~~~units~~~~} \\
\hline
\\f(x)= ∛x ~~~ ⇒ ~~~ f(x)= ∛(x \normalsize\color{red}{ -~\rm{c}} ) &~\rm{to~~the~~right~} \\
\text{ } \\
f(x)= ∛x ~~~ ⇒ ~~~ f(x)= ∛(x \normalsize\color{red}{ +~\rm{c} }) &~\rm{to~~the~~left ~} \\
\text{ } \\
f(x)= ∛x ~~~ ⇒ ~~~ f(x)= ∛(x) \normalsize\color{red}{ +~\rm{c} } &~\rm{up~} \\
\text{ } \\
f(x)= ∛x ~~~ ⇒ ~~~ f(x)= ∛(x) \normalsize\color{red}{ -~\rm{c} } &~\rm{down~} \\ \\
\hline
\end{array} }}}\)


And we follow the same approach here,

\(\large\color{ blue }{\large {\bbox[5pt, yellow ,border:2px solid white ]{ \large\text{ }\\
\begin{array}{|c|c|c|c|}
\hline~~~~~~~~~~~~~~~~~~~~~~~~~~~\textbf{Shifts}~~~~~~~~~~~~~~~~~~~~~~~~~~~&~\rm{c~~~units~~~~} \\
\hline
\\f(x)= x^{3} ~~~ ⇒ ~~~ f(x)= (x \normalsize\color{red}{ -~\rm{c}} )^{3} &~\rm{to~~the~~right~} \\
\text{ } \\
f(x)= x^{3} ~~~ ⇒ ~~~ f(x)= (x \normalsize\color{red}{ +~\rm{c} })^{3} &~\rm{to~~the~~left ~} \\
\text{ } \\
f(x)= x^{3} ~~~ ⇒ ~~~ f(x)= x^{3} \normalsize\color{red}{ +~\rm{c} } &~\rm{up~} \\
\text{ } \\
f(x)= x^{3} ~~~ ⇒ ~~~ f(x)= x^{3} \normalsize\color{red}{ -~\rm{c} } &~\rm{down~} \\ \\
\hline
\end{array} }}}\)

Answer 2

If you try to find any point the same way as I did for when x= 0, 1, 2, -1, and -2 you will see how any point you find (if you do it correctly) will be on `y=x³+4`.

Now a little bit more instructions,

\(\LARGE\color{darkblue }{\rm {Also,~~~for~~~a~~~future~~~reference:} }\)

\(\normalsize\color{blue}{\rm {you~~~can~~~find~~~any~~~section~~~by:} }\)
\(\normalsize \color{black}{\rm { 1) } }\) clicking "more subjects" (the top left corner, towards the center)
\(\LARGE\color{black}{\rm { 2) } }\) typing in the name of the section (name of a section can be "history" Mathematics and other section for each unique area of studying).

\(\normalsize\color{blue}{\rm {You~~~can~~~FAN~~~someone~~~by:} }\)
\(\normalsize\color{black}{\rm { 1) } }\) clicking on the user's name
\(\normalsize\color{black}{\rm { 2) } }\) clicking "fan" on the bottom right corner of user's box.
\(\normalsize\color{black}{\rm { (~ } }\)You can also write a testimonial by clicking "add testimonial" and
typing something in testimonial box.\(\normalsize\color{black}{\rm { ~) } }\)


\(\normalsize\color{blue}{\rm {You~~~can~~~mention~~~someone~~~in~~~your~~~question} }\) (or in any other question) by writing @ in front of their name, just like I would mention you... LOOK ! .... @SolomonZelman (they would get a notification that a user mentioned them in a reply)


\(\normalsize\color{blue}{\rm {You~~~can~~~ message~~~someone~~~by:} }\)
\(\normalsize\color{black}{\rm { 1) } }\) clicking on the someone's username
\(\normalsize\color{black}{\rm { 2) } }\) clicking "Send Message"
\(\normalsize\color{black}{\rm { 3) } }\) type your message press submit, and wait till the messages submits.

\(\normalsize\color{blue}{\rm {You~~~can~~~ see~~~if~~~a~~~user~~~is~~~offline~~~by} }\)
Clicking on the user's username, and below his
picture you will see (in light blue) “offline”, “online” or you might see that he is viewing or replying to a specific question. You might as well see that he is just looking around in a specific section.

If you have any questions you can message me or anyone else on this website. We will be happy to respond !