What is two or more functions combined to create a new function?
Combining Functions
100
What is the algebraic combination, (f+g)(x) = f(x) + g(x)?
Sum
100
What is domain of 3x - 1?
All real numbers
100
Which of the ordered pairs (1,1) (4, -2) (3, -1) are in the relation given by 3x + 4y = 5?
(3, -1)
100
What are the two functions defined implicitly by the given relation, x^2 + y^2 = 25?
y = √(25- x^2 ) and y= - √(25- x^2 )
200
What is applying one function to the results of of another function?
Composition of Functions
200
What is the algebraic combination, (f-g)(x) = f(x) - g(x)?
Difference
200
What is f(g(x)) and g(f(x)) when f(x) = 3x + 2 and g(x) = x -1?
f(g(x)) = 3x - 1; g(f(x)) = 3x + 1
200
Which of the ordered pairs (2, -5) (1, 3) (2, 1) are in the relation defined by x^2y + y^2 = 5. Is the relation a function?
(2, -5) (2, 1) - this realtion is not a function.
200
What are the two functions defined implicitly by the given relation, x^ 2 - y^2 = 25?
y = √( x^(2 )- 25) and y = - √( x^(2 )- 25)
300
What is a set of ordered pairs of real numbers?
Relation
300
What is the algebraic combination, (fg)(x) = f(x)(g(x)?
Product
300
What is f(x) + g(x) when f(x) = 2x and g(x) = x -1?
f(g) + g(x) = 3x -1
300
Which of the ordered pairs (5,1) (3,4) (0, -5) are all in relation given by x^2 + y^2 = 25?
(3,4)
300
What are the two functions defined implicitly by the given relation, x + |y| = 1?
y = 1 - x and y = x -1
400
What is a function that is a sunset of a relation defined by an equation in x and y?
Implicitly defined function
400
What is the domain of the new function of sum, difference, product, and quotient?
All real numbers
400
What is the formulas for (f/g) (3) and (g/f)(-2) when f(x) = 2x - 3 and g(x) = x + 1?
5; -6
400
What is an ordered pair?
A pair of real numbers (x,y).
400
What are the two functions defined implicitly by the given relation, y^2 = x^2?
y = x and y = -x or y = |x| or y = -|x|
500
What is the vertical line test?
Each vertical line drawn through the graph will intersect a function in only one location.
500
What is the algebraic combination, (f/g) (x) = f(x)/g(x)?
Quotient
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?
No
500
Which of the following relations relaions defines the function y = |x| implicity?
A. y + or - x
B. y^2 = x^2
C. y^3 = x^3
D. x^2 + y^2 = 1
E. x = |y|