FUNCTION FAMILIES

Families by Graph Features

100

This function family's graphs repeat themselves over a constant cycle. They are wavy shaped.

Trigonometric Functions

200

This function family's graphs make a smooth curve. They change direction and have a minimum or a maximum. The rate of change is not constant.

QUADRATIC

300

The graphs in this function family change direction (increasing/decreasing), and they are made of two straight lines. They have a minimum or a maximum.

ABSOLUTE VALUE

400

This function family's graphs has a smooth curve and   a domain of (0, + infinity) 

They either increase or decrease only and do not change direction, and the rate of change increases or decreases.

EXPONENTIAL

500

This function family graph has vertical and horizontal asymptotes and its end behavior is 

as x --> + infinity, f(x) --> + and - infinity

as x --> - infinity, f(x) --> + and - infinity

RATIONAL FUNCTIONS

Function Equations (name the family)

100

f(x)= -2x + 4

LINEAR

200

f(x)=|8x-2|-3

ABSOLUTE VALUE

300

A(t)=2,000(1.02)^t

EXPONENTIAL

400

g(x)= (x+2)(x-3)

QUADRATIC  (in factored form)

500

f(x) = (x+3)(x-4)(x+2)(x+1)²

POLYNOMIAL  

(Bonus: what degree is it?)

Function Transformations

100

Parent function: y = x

Graph moved up 3 and got twice as steep

What is the new equation?>

y = 2x + 3

200

Parent function: y = sin x

Graph moved down 2 and the waves are now 4 high

What is the new equation?

y = 4 sin x - 2

300

Parent function: y = x²

The graph moved left 3, got twice as wide, and moved down 2... What is the new equation?

y= 1/2(x+3)² - 2

400

Transformed function is y = 2^(x-3)

The parent function was 2^x

How did the graph change from the original function? Describe the transformation 

It moved right 3

500

The new function is

f(x)= -20 cos (x) +3

How did it change from the original function, y=cos x?

It flipped upside down, the amplitude is now 20 (so the waves are 20 from midline to top/bottom, and the midline is 3

Function Family Clues

100

Functions in this family have a variable in the exponent.

Exponential functions

200

You can use right triangles OR the unit circle to find these functions for different angles.

Trigonometric Functions

300

These functions are the inverse functions of exponential functions.

Logarithmic Functions

400

These equations have a root over the variable

Radical Functions

500

The equation is in the form 

a_nxⁿ+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+ . . .a₀

Polynomial Functions (with degree n)

Evaluate the function

100

f(x) = 4x - 6

Evaluate for x = 4 

f(4) = 10

200

g(x)= 3|x+2|

Evaluate for x = -5

g(-5) = 9

300

f(x)= log₂x

Evaluate for x = 32

f(32) = 5

400

h(x) = (x-2)/(x+2)(x-3)

Evaluate for x = -3

h(x)= undefined!!  (can't divide by zero)

500

f(x) = 3^x+2 - 7

Evaluate for x = 2

f(2) = 74