Functions

FUNCTION BASICS

100

Question:
A function assigns each input exactly how many outputs?

What is exactly one output

200

Question:
In y=f(x), what is the independent variable?

What is x

300

Question:
If f(x)=3x²+2x-1, find f(-2).

What is 7

400

Question:
If f(x)=x²-3x+5, find f(1).

What is 3

500

Question:
If f(x)=3x²+2x-1, find f(a+h).

3a²+6ah+3h²+2a+2h-1

DOMAIN & RANGE

100

Question:
The set of all possible input values of a function is called what?

What is the domain

200

Question:
The set of all possible output values is called what?

What is the range

300

Question:
What is the domain of 

f(x)=sqrt x

[0,Infity)

400

Question:
Find the domain of

f(x)=\sqrt{3x+2}-1.

[-2/3,Infity)

500

Question:
Find the domain AND range of

f(x)=(x-4)²+5.

Domain:

(-infty,infty)

Range:

[5,\infty)

GRAPHS & INTERCEPTS

100

Question:
What test determines whether a graph represents a function?

What is the vertical line test?

200

If a vertical line crosses a graph twice, is the graph a function?

What is no?

300

Question:
What is an x-intercept?

What is a point where y=0

400

Question:
What is a y-intercept?

Answer:
What is a point where x=0

500

Question:
Can a function have multiple x-intercepts but multiple y-intercepts?

What is yes to multiple x-intercepts, but at most one y-intercept?

COMBINING FUNCTIONS

100

Suppose:

f(x)=2x-3 and g(x)=x² -1.

What does (f+g)(x) mean?

f(x)+g(x)

200

Suppose:

f(x)=2x-3 and g(x)=x²-1.

Find

(f+g)(x).

(2x-3)+(x²-1)

x²+2x-4

300

Suppose:

f(x)=2x-3 and g(x)=x²-1.

Find

(f-g)(x).

(2x-3)-(x²-1)

-x²+2x-2

400

Suppose:

f(x)=2x-3 and g(x)=x²-1.

Find

(fg)(x).

(2x-3)(x²-1)

2x³-3x²-2x+3

500

Suppose:

f(x)=2x-3 and g(x)=x²-1.

Find the domain of

f(x)/g(x)=2x-3/x²-1

The denominator cannot equal zero:

x²-1 not equal 0

(x-1)(x+1) not equal 0

Therefore:

x not equal 1,-1 or (-infty,-1)u(-1,1)u(1,infty)

COMPOSITION

100

What does (f o g)(x) mean?

f(g(x))

Think: g goes inside f.

200

Question:

f(x)=x²

and

g(x)=3x+1

find

(f o g)(x).

f(g(x))=(3x+1)²

(3x+1)²

300

f(x)=x²

and

g(x)=3x+1

find

(g o f)(x).

g(f(x))=3x²+1

3x²+1

400

Question:
True or false:

(f o g)(x)=(g o f)(x)

for every pair of functions.

What is FALSE?

500

Question:
A store gives 20% off an item, then a coupon gives an additional 15% off the sale price. If the original price is x, what percentage of the original price does the customer ultimately pay?

First:

0.80x

Then:

0.85(0.80x)

=0.68x

So the cust