Intro to Functions
Define the following terms...
Function -
Domain -
Range -
Function - A relationship between 2 sets of values, where each input has one corresponding output
Domain - A set of values that represent the inputs of a function.
Range - A set of values that represent the outputs of a function
What happens when you add a constant to a parent function?
f(x)+c
It moves up by c.
What is a composite function?
2 functions combined where the output of one is the input of another. Or a function inside a function.
Combine like terms:
9xy+x^4-3-xy+4x^4
=5x^4+8xy-3
Write the following equation in function notation, name the function f(x)
y - x^2 = 9x +6
f(x) = x^2 +9x+6
what happens when you add c to x in a function?
f(x+c)
Create a piecewise function where x=0, and f(x) is the input of g(x).
g(f(0))
Distribute
5x(x^2+3)
5x^3+15x
What is the range of the following function?
function: {(2,1),(3,2),(4,3),(5,4),(6,5), (7, 0), (8,-1)}
R: {-1, 0, 1, 2, 3, 4, 5}
Draw x^2+1
x^2 graph but shifted up 1
Determine the final output of the following function: f(g(2))
f(x)= x^2+1
g(x)=3x+2
f(g(2))=65
Factor out the GCF.
4x^4+2x^2
2x^2(2x^2+1)
What is the domain of the following function in interval notation? (Take a hint for -100 pts)
f(x)={ x2 if -4<x<3, x-1 if x≥ 3
D: (-4,infinity)
Graph f(x)= 1/x and tell me what the V.A. and H.A. are.
V.A.: x=0
H.A.: y=0
find f(g(x)), where x=0
f(x)=x+1
g(x)=e^x
f(g(x)=(e^x)+1
when x=0
e^x= 1
f(g(0))= 2
FOIL and simplify.
(x+3)(x-3)
x^2-9
What is the Range of the following function in interval notation? (Take a hint for -100 pts : I'll draw the graph)
f(x)= x-1
R: (- inf., 0) U (0, inf.)
What is the range of the following function?
f(x)=e^x
R: (0, inf.) because it cannot have negative values.
Determine the output of the following functions:
f(x)=g(x)
f(x)=x^2+12
g(x)= 7x
0= x^2 -7x+12
(x-3)(x-4)=0
x=3,4
What are the sides needed to find sin(theta)?
Opposite and Hypotenuse.