Piecewise Functions

[whole stratus]

What do I do

[eager heath]

You have to graph a function.

If you have conditions connected via bracket like on this example, you have to draw 2 functions:

1. First one f(x) = 4x + 15 should go from negative infinity to -5.
2. Second one f(x) = x - 3 should go from 2 to infinity.

Remember to add unfilled circles at -5 and 2 points.

[whole stratus]

i dont get it

[late gust]

what part of it

[whole stratus]

like how to graph it

[late gust]

you mean the software or the graph itself

[whole stratus]

the graph

[eager heath]

You can use GeoGebra to look up, how they actually look and see how they're changing.

[whole stratus]

desmos?

does that work

[eager heath]

Also an option.

[whole stratus]

i can plug it in?

[eager heath]

I use GeoGebra a bit more often, but desmos is also a good option.

[eager heath]

Yeah, desmos is pretty good for checking out how functions should be graphed.

[whole stratus]

nvm

i dont think it will work

[eager heath]

Also, do you have an issue with the split or how these function should be described on the graph?

[whole stratus]

idk how to draw it on the graph

[eager heath]

First of all, do you know how to graph both of these functions:

1. f(x) = 4x + 15
2. f(x) = x - 3

[whole stratus]

how?

[eager heath]

If someone has told you to just draw it on a graph, without any other catches.

[whole stratus]

not sure how

[eager heath]

f(x) = 4x + 15

This basic function is a linear function. It's base form is:

ax + b

a tells you, by how much y increases in a single x, while b is just an offset.

[whole stratus]

ok

[eager heath]

This is an example:
-# f(x) = 2x + 4

Function increases (y value) by 2 every single (x). Function's offset is 4, because if you would use x as 0, then it would simply equal 4.

Your equation (4x + 15) is pretty similar. It goes up by 4 every single x, and it's offset is 15. Try drawing it on your own.

[whole stratus]

but idk what the x<-5 means

:(

[eager heath]

You just have to draw this function for points where x is smaller than 5.

[whole stratus]

is f(-6) = -9 good

[eager heath]

Yes.

To make it easier, you can draw entire function, then just cut it off for x that are higher than -5.

[whole stratus]

where do i graph that>

im so confused plz help

[eager heath]

On this graph. Calculate for points like -5, -6, -7, -8 and connect them.

[whole stratus]

is just one point fine

i already did (-6,-9)

for second, f(3) = 0

so I guess (0,3)

[eager heath]

Do not calculate for points that are higher than -5.

[whole stratus]

for bottom one

x-3

[eager heath]

There's nothing between -5 and 2.

[whole stratus]

wdym

oh

idk how to do it

[eager heath]

Are you sure that you're familiar with linear functions? If you aren't, then I think it'll be pretty hard to explain this exercise to you.

[whole stratus]

I am

y = mx+b

[eager heath]

Just imagine you have to draw function f(x) = 4x + 15 , but only for points where x is less than 5.

[whole stratus]

what does that mean

how is this correct?

can u help

[whole stratus]

?

is this correct

[onyx yarrow]

no

[onyx yarrow]

$$
f(x)=\begin{cases}4x+15&x;\xr{<};{-5}\x-2&x;\xr{>};3\end{cases}
$$

[muted harness]

tota nox

[onyx yarrow]

ok

so

,tikz
\draw [gray] (-10.5, 10.5) grid (10.5, 10.5);
\draw [thick, <->] (0, -10) -- (0, 10);
\draw [thick, <->] (-10, 0) -- (10, 0);

[muted harness]

tota nox

[onyx yarrow]

ok i give up

so

[eager heath]

2nd equation is wrong.

It's x + 3 when x < 2.
You wrote -x + 3

[onyx yarrow]

mb