Building Functions: Precalculus

Function Composition

100

Function Composition

f(x) = x + 2

g(x) = 4x

f(g(x))

What is 4x + 2?

200

Function Composition

f(x) = 2x – 3

g(x) = x + 1

f(g(x)) Simplified!

What is 2x – 1?

300

Function Composition

f(x) = 3x + 2

g(x) = 2x²

f(g(x))

What is 6x² + 2?

400

Function Composition

f(x) = 3x + 2

g(x) = x²

g(f(x)) simplified!

What is 9x² + 12x + 4

500

Function Composition

f(x) = x + 1

g(x) = 2x

h(x) = x²

f(g(h(x)))

What is 2x²+1?

Parent Functions

100

Parent Functions

What 3 parent Functions are bounded?

what is 

y= 1/(1+e^-x), y=sin(x), y=cos(x)

200

Parent Functions

All Parent Functions that are Even.

What is 

y=x^2, y=abs(x), y=cos(x)

300

Parent Functions

All Parent Functions with extrema.

What is 

y=x^2, y=abs(x), y=sin(x), y=cos(x)

400

Parent Functions

All family functions that has an asymptote.

What is 

y=1/x, y=b^x, y=log(x), y=1/(1+e^-x)

500

Parent Functions

Given 

a abs(x-h) +k

The a, h, and k do what to the graph? 

full credit- name 3 for a, 2 for h, and 2 for k

What is

a compresses(narrows) or stretches (widens) 

-a flips over the x axis.

h shifts the graph left or right (horizontally)

k shifts the graph up or down (vertically)

Domain and Range

100

Domain and Range

What is the domain of y=x

what is 

(-oo ,oo )

200

Given 

f(x) = x^2 and g(x)=sqrt(x)

What is the domain of f(g(x))

What is

[0,oo)

300

Domain and Range

The range of this function:

f(x) = x² - x + 12

What is (11.75, oo )?

400

Domain and Range

The domain of this composition:

f(x)=log(15-x) +3 , g(x)=x^3 , g(f(x))

What is 

(-oo , 15)

500

Domain and Range

The Domain for:

(sqrt(-x+2)ln(x+2))/(x^2-4)

What is 

(-2,2) ?

Functional Inverses

100

Find 

g^-1(x)

given g(x)=

1/x -2

What is 

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

200

Inverse Functions

The inverse of the cube root function.

What is the cubic function?

300

Inverse Functions

The reason the inverse of the points below is not a function:

(1, 4), (-3, 5), (2, 4), (1, 4)

What is there is more than one output for the input of 4?

400

Inverse Functions

The inverse function for 2x³ + 3.

What is 

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

?

500

Inverse Functions

Verify these are Inverses

f (n) = −(n + 1)^3

g(n) = 3 + n^3

What is NO?

Evaluate Composition

100

Given f(t)=

t^2 -t

 and h(x)=3x+2

Evaluate f(h(1))

What is f(h(1))=20 ?

200

If f(x)= 3x-5 

and 

g(x)=

X^2

find f(g(3))

What is f(g(3))=22 ?

300

If f (x) = −9x − 9 

and 

g(x)=

sqrt(x-9)

find f(g(10))

What is f(g(10))=-18 ?

400

If f(x) = 

6x^2-2x

and

g(x) =

3-1/x + 3/x

find f(g(2))

what is f(g(2))= 88?

500

If f(x) = 

(x^3+11)/(x^2-1)

and g(x)=15x-5x-1

and h(x)=

sqrt(x)-abs(x-59)

find h(g(f(4)))

What is h(g(f(4)))=-3 ?