Question

@mathslover
Interactive tutorial if you must?

Answer 1

I'll give you like a basic lecture or what ever you want to call it. Tutorial?

I'll include:
Function Notation, Basic Function Graphs
Translating Graphs and Inverse Functions
Vertical Reflections and Scalings
Horizontal Reflections and Scalings
Reciprocal Graphs

That sound decent enough?

Answer 2

Sounds well. :-)

Answer 3

Function Notation:

f(x) = x-7 f of x equals x minus seven
g(x) = 3x^2 g of x equals three x squared
f(2) = (2)-7=-5 f of two equals negative five
f(a) = (a) - 7 = (a-7) f of a equals a minus seven
f(g(x)) = (3x^2)-7 f of g of x equals three x squared minus seven

Given the function f(x) = x^2, rewrite each of the transformed functions as an equation, and then evaluate & simplify.

f(-2) = ?
f(x) + 2 = ?
f(x+2) = ?
3f(x) = ?
f(3x) = ?
f(1/3) = ?

As always take your time.

Answer 4

f(-1) = 4 ; f of negative 1 equals four.

f(x) + 2 = x^2 + 2 ; f of x plus two equals x square plus 2

f(x+2) = (x+2)^2= x^2 + 4 + 4x ; f of (x+2) equals x squared plus 4 plus 4x

3f(x) = 3x^2 ; 3 times f of x equals 3 times x squared.

f(1/3) = 1/9 ; f of 1/3 equals 1/9

Is this what you asked for? ^

Answer 5

o.O f(-2) = 4

Answer 6

Nvm, I was looking at f(3x) and saying oh what the heck then realized you missed that one, but it's fine lol. We can move on to transforming functions, there's not much else for function notation.

Answer 7

oh .. yeah :P Sorry .. I missed that one. f(3x) = 9x^2 ..

Answer 8

Yup, that's right.

Answer 9

Alright so for transformed functions, they are in the form of:

\[y= a \times f(b(x-h))+k\]

I'll make a little table for you:



You'll have to memorize these.

For these basic functions; a = 1, b = 1, h = 0, k = 0

So, we'll graph these functions using tables of value in order to see the patterns that arise as change the a, b, h, and k.

To graph using a tables of values, means we substitute one variable into a function to find the value of a certain variable. So when we use the first number chosen to find the second value it's called the independent variable, as it is independently chosen for the certain equation, while the second number, found as the solution of the equation, is the dependant variable. The dependant variable, is usually represented by y, relies upon the chosen value of the independent variable, in this case x. You probably know this already, but it's a good refresher. It's best you memorize how these functions look like.

We'll start off with f(x) = x^2, graphing y = f(x) and write the domain and range.

http://puu.sh/9n64K/86dec2cae7.png

\[D: \mathbb{R} ~~~~~ R: y \ge 0\]

Basic function: f(x) = x^2
Transformed function:
\[y=a \times (b(x-h))^2+k\]

While I draw the basic function table again and take a puush of it -.-, do this problem.

For the following transformed function, write the transformed function in functional notation, and determine the values of a,b, h, and k.

\[y = -\frac{ 1 }{ 3 }(x+3)^2-2\]