Functions

Question 1

define a mapping

Answer 1

a mapping is a rule that assignes an input value x to one or more output values y

Question 2

define a function, and what test can be done on a function to determine if it is a function

Answer 2

a function is a mapping where there is only one y value for each x value.
Vertical line test

Question 3

What is the difference between a one to one function and a one to many function

Answer 3

a one to one function is a function in which every y value correlates with only one x-value.

a one to many function is a function in which several x values create the same y value

Question 4

define the domain of a function

Answer 4

the set of allowed inputs into a function

Question 5

define the range of a function

Answer 5

the set of possible outputs of the function

Question 6

if you apply the function g(x) to the function f(x), what is the output function you get

Answer 6

f(g(x))

Question 7

for a function y=f(x), how do you find the inverse of the function?

Answer 7

re-arrange y = f(x) into the form x=f(y),
replace ys with xs and xs with ys an lable the function f^-1(x)

Question 8

what transformation is same is finding the inverse of a function

Answer 8

reflection in the line y = x

Question 9

f(f^-1(x))=..

Answer 9

f(x)

Question 10

the domain of f^-1(x) is the same as the …

Answer 10

range of f(x)

Question 11

the range of f(x) is the same as the …

Answer 11

domain of f^-1(x)

Question 12

The range of f^-1(x) is the same as the …

Answer 12

domain of f(x)

Question 13

the domain of f(x) is the same as the

Answer 13

range of f^-1(x)

Question 14

for a function to have an inverse, what type of function must it be?

Answer 14

one to one

Question 15

if a function is many to one? what needs to be done to it such that an inverse can be applied?

Answer 15

the domain needs to be restricted to a point where the function is one-to-one for its defined domain.