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Transformations
Domain and Range
Composition of functions
linear and quadratic functions
100

Determine the type of transformations of the basic function. 

f(x) = x2 -6

Down 6 units 

100

Find the domain. 

f(x) = -3x + 4

All real numbers

100

Find ( f + g) (x)

f(x) = 2x      g(x) = x + 3

3x + 3

100

Find the slope and y-intercept

f(x)= -1 - 1/8 x

slope= -1/8

y-intercept ( 0,-1)

200

Determine the type of transformations of the basic function. 

f(x)= (x-3)3 + 2

Right 3 units, up 2 units 

200

Find the Domain

f(x)= x2 + 3

All Real Numbers

200

Find ( f 0 g) (x) 

f(x) = x + 5     g(x) = x2 + 4

x2 + 9

200

Determine if the function has a maximum or a minimum 

f(x) = -2x2 -20x - 48

Maximum 

300

Determine the type of transformations of the basic function. 

f(x)= 2(x+1)2

 Stretch of 2 units

Left 1 unit  

300

Find the Range 

f(x) = x2 + 3

[3, positive infinity)

300

Find ( f 0 g)(x) 

f(x) = x3 + 3        g(x) = x3

x9 + 3

300

Find the value of the max or min of the function. 

f(x) = -2x2 -20x - 48

Occurs at x = _______ 

Occurs at x = -5

400

Determine the type of transformations of the basic function. 

f(x) = - (x-4)2 + 2

Reflection over the x-axis

Right 4 units

Up 2 units 

400

Find the domain

f(x) = Square root ( x+1) +6

[-1,positive infinity)

400

Find ( g 0 f ) 

f(x) = x + 5     g(x) = x2 + 4

x2 + 10x + 29

400

Write the linear function with the following properties. 

f(4) = 9

slope of f = -6

y= -6x + 33

500

Determine the type of transformations of the basic function. 

f(x) = 2+ 1/3(x+2)3


 Compression 1/3 units

Left 2 units

Up 2 units 

500

Find the domain.

f(x) = -11/ ( x+9)

(- infinity, -9) U ( -9, positive infinity) 

500

Find ( f 0 g) (4)

f(x) = x2     g(x) = -4x -2

324

500

The total revenue of Joe's Realty is given as the function R(x) = 200x - 0.2x2, where x is the number of the rooms filled.  What number of rooms filled produces the maximum revenue? 


500 rooms