Chapter 1 Functions and Models Flashcards
What is a function?
A funciton f is a rule that assigns to each element x in a set D exactly one element called f(x), in a set E.
Domain
All elements of x or all the possible inputs
Range
All elements of y or all the possible outputs
Independent Variable
Arbitrary number in the domain of a function
Dependent Variable
A symbol that represents a number in the range of the function
What are the four different ways to represent a function?
Verbally
Numerically
Visually
Algebraically
y = f(x) + c does what?
shifts the graph f(x) a distance of C units upwards
y = f(x) -c does what?
shifts the graph f(x) a distance of C units downward
y = f(x+c) does what?
shifts the graph f(x) a distance of C units to the left
y = f(x-c) does what?
shifts the graph f(x) a distance of C units to the right
y = c f(x) does what?
stretches the graph vertically by a factor of C
y = (1/c) f(x) does what?
shrink the graph vertically by a factor of C
y = f(cx) does what?
shrink the graph horizontally by a factor of C
y = f(x/c) does what?
stretch the graph horizontally by a factor of C
y = -f(x) does what?
reflect the graph across the x-axis
y = f(-x) does what?
reflect the graph across the y-axis
b^x+y =
b^x * b^y
b^x-y =
b^x / b^y
(b^x)y
b^xy
(ab)^x
a^x * b^x
f(x) is one-to-one when?
it never takes on the same value twice
what is an inverse function?
f^-1 (y) = x
f(x) = y
log b (xy) =
log b x + log b y
log b (x/y)
log b x - log b y
log b (x)^r
r log b (x)
ln x =
log e (x)
e ^ ln (x) =
x
x^r =
e^ r ln x
change of base formula
log b x = ln x / ln b
