Functions

Function Definitions

100

What are three ways to represent a function rule?

Graph, chart, algebraic expression, words.

200

What is a functions domain?

The set of all possible input values to a function

300

What is a functions range?

The set of all possible output values of a function

400

How many vertical intercepts can a function have?

Only one: f(0) is unique.

500

What are the roots of a function?

The Horizontal intercepts, or solutions to f(x)=0

Domain/Range/Intercepts

100

What is the domain of the function f(x) = 3/(x-2)?

x is not 2, or in interval notation (-oo,2),(2,oo)

200

What is the range of the function f(x) = x² ?

x >=0 or in interval notation [0,oo)

300

What is the vertical intercept of the function f(x) = x³-2x+9

f(0)=9

400

What is the horizontal intercept of f(x) = x-2?

f(x)=0=x-2 means x=2

500

What are the vertical and horizontal intercepts of this function? (Desmos)

Vertical: f(0) = 6

Horizontal: f(x)=0, means x=-3, x=-1, x=1, x=2

Function Composition

100

Using the charts, what is f(g(0))

f(g(0))=f(-1)=0

200

using the charts what is g(g(4))?

g(g(4))=g(6)=11

300

f(x) = x²

g(x)=x+1

what is g(f(2))?

g(f(2))=g(2²)=g(4)=4+1=5

400

using the charts, solve for x:

g(f(x))=-10

g(?) = -10

?=-4=f(x)

f(x)=-4

x=0

500

f(x)=x²

g(x)=x⁴

What is g(f(x))?

g(f(x))=g(x²)=(x²)⁴=x⁸

Creating Functions/Word Problems

100

let x = the side length of a 3d cube and V = the volume of the cube. Define a function g that has x as an input and V as an output. Write the function rule in terms of x

g(x) = V

g(x) = x³

200

let h be a function that takes in a variable t representing the number of years since a tree was planted, and outputs the height of the tree at time t. 50 years after it was planted there is a wildfire and the tree falls. Draw an approximate graph for this function. Make sure to label the axes. 

(should be increasing up until year 50, then suddenly decreases)

300

Sally is filling up her pool. Let t be the number of minutes that have passed since she began filling the pool.  The function h(t) = 12t + 12 represents the height of the water at time t, where height is given in inches. How long after she started filling the pool will the water be 3 feet deep? (Pay attention to units)

h(2)=12*2 +12 = 12*3 means the water is 3 feet deep (12 inches in a foot) so the water will be 3 feet deep after 2 minutes

400

A certain database uses a function named g to access the population of Loveland, CO and uses Jan 1 1990 as its reference time. so P=g(u) represents Loveland's population u years from Jan 1, 1990. Use function notation to represent Loveland's population on 1/1/1970

g(-20) 

500

A certain database uses a function named g to access the population of Loveland, CO and uses Jan 1 1990 as its reference time. so P=g(u) represents Loveland's population u years from Jan 1, 1990. What does g(8)-g(-10) represent?

this is the change in population of loveland from 1980 to 1998.