FUNCTIONSWe put the FUN in functions!!!!

FunctionsDefinition: a relation in which each element ofthe domain is paired with exactly one elementof the range.You decide: Yes or no?

x y

4 2

3 5

-2 -2

3 4

8 10

x y-3 3-2 30 42 44 4

x y

6 35 -22 3

12 -127 3

x y

-4 12

5 9

-4 8

3 6

6 3

Functions

Is this a function?

Is this a function?

Is this a function?

FunctionsIs this a function?

Is this a function?

Is this a function?Is this a function?

FunctionsDomain: all the x values or inputvalues for a functionD = {1,2,3,4}

Range: all the y values or outputvalues for a function R = {3,5,7,9}

x y1 32 53 74 9

FunctionsWe write functions a little differently thanregular equations.

f(x) = 15x f(x) is read the function of x The input x is any or f of x. It is the output or number. It is the domain. range value.

Function NotationFind f(4) for f(x) = 2x + 1 meansWhat is the value of the functionwhen x = 4.In this example you replace x inthe equation with 4.f(x) = 2(4) +1 9f(4) = 9

Find f(6) for f(x) = 2x + 1 meansWhat is the value of the functionwhen x = 6.In this example you replace x inthe equation with 6.f(x) = 2(6) +1 13f(6) = 13

Find f(10) for f(x) = 2x +1f(x) = 2(10) +1

f(10) = 21Therefore f(10) = 21

We input 10 and the output is 21.

Find f(-7) for f(x) = 2x +1f(x) = 2(-7) +1

f(x) = -13Therefore f(-7) = -13

We input -7 and the output is -13.

Find f(-4) for f(x) = 2x +1f(-4) = -7Find f(-10) for f(x) = 2x +1f(-10) = -19Find f(3) for f(x) = -3x -8f(3) = -17

Which will increase the volume of a cylinder more quickly: increasing

the radius or increasing the height?

FunctionsThe cylinder below has a radius of 1 inch and a heightof 3 inches. Find its volume. What would happen to the volume if you increasedthe radius in one increments, but kept the height thesame? Use the table for your data. Height (h) Volume

(cubic in)

1 in2 in3in4 in5 in6 in7 in8 in

FunctionsIs this a linear relationship? How do you know?Graph the relationship between radius and volume onyour graph paper?

At what radius would the volume be 100 cubic inches?

How can you tell if the relationship is a function bylooking at the table?By looking at the graph?

Hiking Trip

Bruneau sand dunes hike: We walked 3/5 a mile in 3/4 of an hour and kept that same pace for the day.

The following information comes from three different hiking trips the group went on last year. Can you identify how many miles per

hour the groups hiked on each trip?

Stanley Lake Hike

Time Distance Traveled

7:00 – 8:30 2.25 miles

8:30 – 11:00

3

Graph from the Bogus Basin Hike