Question

I am studying my lesson on function notation, can anyone tell me how to graph them. I'd really appreciate it! =)

Answer 1

do you have some specific question or just explanation

Answer 2

@KayleeNeedsHelp

Answer 3

Just explain plz

Answer 4

Okay, so say you have the simple function of
\[f(x) = x^2+1\]
All you would do is plug in values for x and solve for f(x).
\[f(0) = (0)^2 + 1 = 1\]
This would be your first coordinate: (0,1)
Repeat several times with a variety of different x-values, such as 0, -1, 1, -2, 2, etc.
Of course, it is always good to know about parent graphs and what they look like. Every single graph in the world resembles its parent graph. Like the example I showed.
f(x) = x^2 + 1 is just a vertical translation one unit up of the graph of f(x) = x^2
There are 7 basic parent functions. (of course there are others, but you won't ever see them in school)
linear - x
quadratic - x^2
cubic - x^3
square root - sqrt(x)
piecewise - [[x]]
rational - 1/x
absolute value - |x|

each parent function has a basic look. see attachment
There are also indicators of translations,etc, which I don't really feel like going into right now lol

Answer 5

But anyway, back to plugging in values for x and solving for f(x). Once you have several points graphed, connect the dots. The more dots, the more accurate the graph. But this is why it is good to know the general shapes of certain graphs so that you can connect the dots easier.
A good online graphing calculator is https://www.desmos.com/calculator

Answer 6

WHOA that was even more than I was expecting for, your great at explaining! THANKS!

Answer 7

'
it is read as f of x (This does NOT mean f times x)means function notation of equation
for example y =2x -2 is a equation
but its also a function
f(x) is another way of representing the "y" variable in an equation.
if we want to write that as function we just need to write f(x) instead of y
so f(x) = 2x -2
for example solve this function when f(2) its mean x is 2 so replace that with x
our function is f(x) = 2x -2
f(2) = because f(2) f(x) ---> f(2)
f(2) = 2(2) -2
we don't have to use left side 2 which is with f like this one f(2)
just deal with right side multiply 2 times 2
= 4-2
now subtract 4 -2 f(2) = 2
so our answer is 2

Answer 8

The picture in the attachment doesn't have an example of a piecewise function. Instead it has an exponential function, which is f(x) = 2^x

Answer 9

Well, thanks, I will look forward to speaking to you often, love your explanations and ideas!

Answer 10

and like @Nnesha said, f(x) is another version of "y"

Answer 11

Nnesha, thank you as well, you help a lot

Answer 12

I was wondering...could I have a medal? I know I didn't really solve anything but I did type a lot lol

Answer 13

Thank you :)

Answer 14

Glad to!

Answer 15

its my pleasure :)