What is two or more functions combined to create a new function?
Combining Functions
100
What rule is this combination? (f+g)(x)=f(x)+ g(x)
The sum rule
100
What is the domain of 4x-1?
All real numbers
100
Which of the ordered pairs; (3,5) (8,-7) (3,-1) are in the relation given by 3x+4y= 5?
(3,-1)
100
Given f(x) = 2x + 3 and g(x) = –x^2 + 5, find (f o g)(x).
–2x^2 + 13
200
What is applying one function to the results of another function
Composition of functions
200
What is this combination? (fg)(x)= f(x)(g(x))
The product rule
200
What is f(g(x)) and g(f(x)) when f(x)= 4x+2 and g(x)= x-2
f(g(x))= 4x-6; g(f(x))=4x
200
Which of the ordered pairs (2,-5) (6,0) (2,1) are in the relation defined by x^2y+ y^2= 5? and is the relation a function?
(2,-5) and (2,1), no the relation is not a function, has two y values for one x value.
200
f(x) = 2x + 3 and g(x) = –x^2 + 5, find (g o f )(x).
–4x^2 – 12x – 4
300
What is a set of ordered pairs of real numbers?
Relation
300
What is the combination? (f-g)(x)= f(x)- g(x)
The difference rule
300
What is f(x)+g(x)= 3x and g(x)= x-2
f(x)+g(x)= 3x+ (x-2)
300
Which of the ordered pairs (5,6) (3,4) (3, -8) are all in relation given by x^2 + y^2 = 25?
(3,4)
300
f(x) = x^2 - 4x + 4; g(x) = x + 1; Find (f o g )(x).
x^2 -2x +5
400
What is the definition of composition of functions?
Applying one function to another function
400
What is the domain of the new functions of sum, difference, product, and quotient functions?
All real numbers
400
What is the f(x)/g(x) when f(x)= 2x and g(x)= 10x
f(x)/g(x)= 2/10= 1/5
400
What is an ordered pair?
A pair of real numbers (x,y).
400
f(x) = x/(x+1) ; g(x) = 1/(x-2); Find (f o g )(x).
1
500
What is the vertical line test?
An imaginary vertical line where you move it around the function, to be a function the line must intersect the function in only one spot at all times.
500
What is the combination? (f/g)(x)= f(x)/g(x)
The quotient rule
500
True or False? The domain of the quotient function (f/g)(x) consists of all numbers that belong to both the domain of f and the domain of g. Justify your answer.
False, x is not the domain of (f/g)(x) if g(x)= 0
500
If the equation relates two different y-values (Such as -5 and 1) to only one x-value (such as 2), is the relation a function?