Chapter 2 Functions Flashcards
What is the domain of a function?
The set of input values which yield an output value
What is the range of a function?
The set of corresponding output values to a given set of input values
Which axis can you find the domain and range?
The x-axis is the domain and the y-axis is the range
What is a piecewise defined function?
A function that employs a different formula on different parts of its domain
What is bracket Notation used for?
To express a piecewise function
{ x+ 1 for x <= 2
g(x) = { 1 for x < 2
What is the absolute value function?
It is a function defined by the following formula
{ x for x >= 0
f(x) = |x| = { -x for x < 0
What is a vertical shift?
It a shift of a function that is done by increasing or decreasing the output y value.
n(x) = O(x) + “vertical units”
How would you shift function’s graph up? Down?
You would shift it up by adding to the output value of the function and you would shift it down by subtracting from the output value of the function.
What is a horizontal shift?
It is a shift of the function’s graph to the right or left
Expressed as
n(t) = o(t+k)
How would you get a function to horizontally shift to the right? To the left?
To shift to the right you would add to input value.
To shift to the left you would subtract from the input value.
What is a Translation?
A vertical or horizontal shift of the graph of a function
What does composition do functions mean?
It means that two or more functions may be connected by the fact that the output of one is the input of the other
g(f(x))
What is it mean to say that f(g(t)) is a composition of f with g?
That the output of g is the input of f
What are inverse functions?
Functions where the input and output have been reversed.
Original —- P=f(t)
Inverse — t = g(p)
What is the notation of an inverse function?
f^-1(t) = p
