Chapters 2&3

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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|