Type of Function

Linear

Exponential

Quadratic

General Equation

Domain

Range

Determined by the location of the horizontal asymptote

Determined by the location of the maximum or minimum y-value

Increasing and Decreasing

Positive slope = increasing

Negative slope = decreasing

Growth = increasing

Decay = decreasing

Has intervals of both increasing and decreasing behavior. The minimum and maximum values divide the increasing and decreasing intervals.

x-intercept

Located where y=0.

All linear functions have an x-intercept, unless the function is a horizontal line.

Located where y=0.

Exponential functions can have zero or one x-intercept.

Located where y=0.

Quadratic functions can have zero, one, or two x-intercepts.

y-intercept

Located where x=0.

All linear functions have a y-intercept.

Located where x=0.

All exponential functions had a y-intercept.

Located where x=0.

Quadratic functions have one y-intercept.

Asymptotes

None

Always horizontal written in the form y=k, where k is a real number.

None

Positive and Negative Intervals

The x-intercept divides the positive and negative intervals, while the slope determines on which side of the x-intercept each interval will be found.

The horizontal asymptote determines whether the exponential function will have any negative values. The x-intercept divides the positive and negative intervals.

The x-intercept(s) will divide the positive and negative intervals. If there is no x-intercept, the quadratic function will have either all positive or all negative values, but not both. If there are two x-intercepts, there will be two positive or two negative intervals.

End Behavior

The slope determines end behavior. Each end goes to infinity in opposite directions.

The ends will always go in different directions, with one end approaching a horizontal asymptote, and the other end going to infinity.

Both ends always have the same end behavior, either going to positive or negative infinity.

Linear

Exponential

Quadratic

• Linear functions are always increasing or always decreasing throughout the domain.
  
• The graph is in the shape of a line.
  
• When the change between x-values is constant, consecutive y-values will also show constant change.

• Exponential growth functions are always increasing and are written with a growth factor of 1+r
  
• Exponential decay functions are always decreasing and are written with a decay factor of 1-r
  
• The graph is in the shape of a steep curve with a flatter portion that approaches a horizontal asymptote.
  
• When the change between x-values is constant, consecutive y-values will increase or decrease at a constant percentage.

• When a quadratic model has a maximum value, the y-values increase before reaching the maximum and then decrease after the maximum.
  
• When a quadratic model has a minimum value, the y-values decrease before reaching the minimum and then increase after the minimum.
  
• The graph is shaped like a U, where each side of the maximum or minimum is a mirror image.
  
• This symmetry can often be seen on a table of values.

Forumas

Variables

Simple Interest

I is interest

P is original Principal

r is the annual interest rate

t is the number of years

Total Balance for Simple Interest

A is the total account balance

P is the original principal

r is the annual interest rate

t is the number of years

Compound Interest

A is the total account balance

P is the original principal

r is the annual interest rate

n is the number of compounding periods in a year

t is the number of years

Continuously Compounded Interest

A is the total account balance

P is the original principal

e is a constant (2.718)

r is the annual interest rate

t is the number of years