Chapters 2&3
Linear functions and their applications
Applications of Linear Equation
Application of linear equations
Mixture Problems
Motion Problems
Geometry Problems
Linear functions
Standard Form:
Ax + By = C
Midpoint Equation:
M = ( x 1 + x 2 2 , y 1 + y 2 2 )
Distance equation:
d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2
Graphing polynomial and rational functions.
rational Functions
Plot graph
vertical asymptotes will divide the number line into regions
Find the horizontal asymptote, if there is one
Find the vertical asymptotes
Find the intercepts
Polynomial Functions
Plot the graph
Determine whether the graph lies above or below the x-axis by picking any value between consecutive x-intercepts and plugging it into the function
Determine which way the ends of the graph point
Plot the x- and y-intercepts on the coordinate plane
Find the zeros for the polynomial
Function operations and compositions
Composition of Functions and Domain
Domain
The resulting set is the domain of f∘g
Specifically, exclude any input x from the domain of g for which g(x) is not in the domain of f
You must find the inputs x within the domain of g for which g(x) is within the domain of f
Find the domain of f
Find the domain of g
Standard Function:
(f∘g)(x)=f(g(x))
Arithmetic Operations on Functions
Division
(f/g)(x)
Multiplication
(fg)(x)
Subtraction
(f−g)(x)
Addition
(f+g)(x)
Basic functions and their transformations
Transformations
f (−x) reflects the function in the y-axis
−f (x) reflects the function in the x-axis
f (x − b) shifts the function b units to the right
f (x + b) shifts the function b units to the left
f (x) − b shifts the function b units downward
f (x) + b shifts the function b units upward
Basic functions
Cubing Function
f(x)=x^3
Squaring Function
f(x)=x^2
Identity Function
f(x)=x
Cube Root function
f(x)=3√x
Square Root Function
f(x)=√x
Absolute Value Function
f(x)=|x|
