Functions

Evaluating a Function

100

Given f(x) = x + 1/x find f(1/x)

1/x + x or (x^2 + 1)/x

200

Given f(x) = x^2 + 1 find f(x+2)

x^2 + 4x + 5

300

Given f(x) = 3x if x < 0 

               = -x^2 if 1 < x < 3 

               = -4 if x > 4 

Find f(2)

-4

400

Given f(x) = x^2 + 1 find f(x) + f(2)

x^2 + 6

500

Given f(x) = x^2 + 1 find (f(x))^2

x^4 + 2x^2 +1

Transformations

100

Rewrite the following function to include the transformations listed. f(x) = x^3 shift up 1, shift left 3

f(x) = (x+3)^3 - 1

200

Rewrite the following function to include the transformations listed. f(x) = x^3 shift down 2, reflect over x-axis

f(x) = - x^3 - 2

300

Rewrite the following function to include the transformations listed. f(x) = x^3 stretch vertically by 2, reflect over x-axis

f(x) = -2x^3

400

Rewrite the following function to include the transformations listed. f(x) = x^3 shrink vertically by 1/2, reflect over y-axis

f(x) = (1/2)(-x)^3

500

Rewrite the following function to include the transformations listed. f(x) = x^3 shrink horizontally by 1/3, shift down 2

f(x) = (3x)^3 - 2

Combining Functions

100

f(x) = 3x - 1;   g(x) = 1/(x + 2) 

Find fg

(3x - 1)/(x + 2)

200

f(x) = 3x - 1;      g(x) = 1/(x + 2) 

Find f/g

3x^2 +5x - 2

300

f(x) = 3x - 1;     g(x) = 1/(x + 2) 

Find the domain of f/g

x ne -2

400

f(x) = 3x - 1;     g(x) = 1/(x + 2) 

Find f(g(x))

3/(x + 2) - 1

500

f(x) = 3x - 1;     g(x) = 1/(x + 2) 

Find g(g(x))

(x + 2)/(5 + 2x)

Inverse Functions

100

Find the inverse of f(x) = x/(x+1)

x/(x - 1)

200

Find the inverse of f(x) = (x+3)/(x-2)

(2x + 3)/(x - 1)

300

Is the following a function? If so, is it one-to-one? f(x) = 2/(x^2 + 1)

Yes, no

400

Are the following functions inverses of each other? 

f(x) = 1/(x - 1) 

g(x) = 1/x + 1

Yes

500

Are the following functions inverses of each other? 

f(x) = (x + 2)/(x - 2) 

g(x) = (2x - 2)/(x + 1)

No

Miscellaneous

100

Find the average rate of change between x = 0 and x = 2 given f(x) = x^2 + x - 1

3

200

Define the term "function"

For each input there is exactly one output

300

Can an equation be one-to-one but not a function?

No

400

Explain the relationship between the domains and ranges of functions and their inverses.

They are opposites

500

List all local minima and maxima for the function: f(x) = 3x + 1/2

None