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Welcome: Please have your math supplies and homework ready. Sec 1.1.3; page 16. Function Notation Domain and Range Intersections of Graphs. Try the following on your calculator and record what your calculator displays. Who is this?. Function Notation.

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sec 1 1 3 page 16

Sec 1.1.3; page 16

Function Notation

Domain and Range

Intersections of Graphs

function notation

Function Notation

Find function values using f(x) notation or graphs.

what is function notation
What is function notation?

Function notation is another way to write “y=“

The notation looks like this: f(x)

f(x) is read “f of x”

solving problems with function notation
Solving Problems with Function Notation

f(x) = 2x + 5, find f(5)

f(5) = 2(5) + 5 Plug in 5 in place of x

f(5) = 10 + 5 Simplify

f(5) = 15 Simplify

This means that when x = 5, y = 15

(5,15)

try this problem
Try this problem

f(x) = -3x + 5, find f(-2)

f( -2 ) = -3( -2 ) + 5

f( -2 ) = 6 + 5

f( -2 ) = 11

other forms of function notation
Other forms of function notation:

Function notation is useful if you are studying more than one function. You may use other letters to describe the function and the variable. The following are some examples: expressed as:

g(x), h(x), or s(t)

They are all used in place of “y=“ .

two functions at one time
Two Functions at One Time

f(x) = 6x + 3 g(r) = 2r – 4

Find the following:

  • f(4) 2. g(-1)

3. g(3) 4. f(0)

Click here to:

See this

problem

worked

Click here to:

See this

problem

worked

Click here to:

See this

problem

worked

Click here to:

See this

problem

worked

for each function determine if there are any restrictions on the values that can be assigned to x
For each function determine if there are any restrictions on the values that can be assigned to x.

I will demonstrate with

k

h- 7

j(x) =

slide13

Domain

The domain of a function is the complete set of possible values of the independent variable in the function.

  • The domain of a function is the set of all possible x-values which will make the function "work" and will output real y-values.
helpful hints
Helpful Hints:
  • When finding the domain, remember:
  • The denominator of a fraction cannot be zero.
  • The values under a square root sign ) must be zero or positive.
slide15

Range

The range of a function is the complete set of all possible resulting values of the dependent variable (y ) of a function, after we have substituted the domain values.

  • The rangeof a function is the possible y values of a function that result when we substitute all the possible x-values into the function.
when finding the range remember
When finding the range, remember:
  • Substitute different x-values into the expression for y to see what is happening. (Is y always positive? Always negative? Or maybe not equal to certain values?)
  • Make sure you look for minimum and maximum values of y.
bestest hint ever
BESTEST HINT EVER:
  • A picture is worth a thousand words.

Graph the function!

examples
Examples:
  • Graphical Examples
  • Not Graphical Examples
first on your calculator and then on your graph paper draw a complete graph of
First on your calculator and then on your graph paperDraw a complete graph of

y=(x+1)(x-3)

State the domain and range of the function.

Make sure to adjust the settings of your calculator if necessary.

ii intersection of graphs

II. Intersection of Graphs

Systems of Equations.

slide28
First on your calculator and then on your graph paperDraw a complete graph functions below, on the same grid.
  • and x-9
find the solution to system of equations
Find the solution to system of equations
  • and x-9

How does graphing two functions and finding the solution to a system of equations related?

system of equations word problem
System of Equations Word Problem
  • Kristin spent $262 on shirts. Dress shirts cost $56 each and Dri-Fit shirts cost $30 each. If she bought a total of 7 shirts then how many of each kind did she buy?
  • What Are our two equations?
  • 56D+30F=262 and D+F=7
solution to word problem
Solution to Word Problem

F=7-D ; We can rearrange one of the equations to solve for one variable in terms of the other

56D+30(7-D)=262 ; we can then substitute this into the other equation, there is only one variable to solve for now!

56D+210-30D=262 ; simplify

26D=52 ; simplify

D=2 ; solve for D

(2)+F=7 ; original equation with our value for D substituted in

F=5; solve for F

This means Kristen bought 5 Dri-Fit shirts and 2 Dress shirts

graph of problem
Graph of Problem

What is the graph telling us?

before you start on your homework
Before you start on your homework…

Make sure you know how to do the following:

Solve for y: x= 3y-4

on your own
On your Own
  • Read and take notes on:

Methods and Meanings on page 18

  • Homework:

R & P

Page 19 #35-41

Due at the beginning of next class period.