FUNCTION NOTATION
A student's height can be represented by a function h, where the input is the students age.
a. What does h(14) represent? Can you determine the units for height?
B. What does h(15)=58 represent? What can you conclude about the units for height?
a. The students height at 14; no the units for the height are not given
b. the height of the student is 58 inches at age 15; the only give the same results
m(x)=4x+15;m(x)=7
x=-2
$77.50
The function c(x)=25x+50 represents the labor costs (in dollars) for Contractor A to build a deck, where x is the # of hours of labor. The table shows sample labor costs from is main competitor, Contractor B. The deck is estimated to take 8 hours of labor. Which contractor would you hire?
Contractor B
A relationship between inputs where each input is related to exactly one output.
Function
h(x)=-7x; h(x)=63
x=-9
You have $99 to buy stamps and envelopes. A sheet of 20 stamps cost $11. A box of 50 envelopes cost $7.50. Write an equation in standard form that models this situation. Do the intercepts of the graph make sense in this context?
11x+7.5y=99 No, you need to buy both stamps and envelopes. The intercepts represent when you do not buy either stamps or envelopes.
Complete the table so it represents a linear function
x_5_10_15_20_25
y_-1_?_?_?_11
The missing numbers are 2,5, and 8
The temperature (in Fahrenheit) x hours after 5pm is represented by t(x)=4x+72. The temperature x hours after 10am is represented by d(x)=4x+72. Describe the transformation from the graph of t to the graph of d.
The graph of d is a reflection in the y-axis of the graph of t.
The set of all possible OUTPUT values of a function
Range
Find the value of x so that the function has the given value h(x)=-7x; h(x)=63
x=-9
Write 23/11 as a decimal
1.2
Determine whether the relation is a function
input|-1 0 1 2 3
output|0 1 4 4 8
function; each input has exactly one output
DALIY DOUBLE FINISH THE LYRIC
I got in one little fight and my mom got scared
She said "you're movin' with your auntie and uncle in bel-air"
.....
I begged and pleaded with her day after day
But she packed my suitcase and sent me on my way
extra 100 for two more verses
The set of all possible INPUT values of a function
Domain
For g(x)-10-8x find the value of x for which g(x)=42
x=4
q(x)=0.5x; q(x)=-4
x=-2
Is the function represented by the ordered pairs linear or nonlinear? (0,2) (3,14) (15,22) (9,38) (11,46)
It's a linear function
The function g(x)=1.0-0.2x represents the percent (in decimal) of battery power remaining on a laptop x hours after it is turned on. The function f(x)=0.75-0.125x represents the percent (in decimal form) of battery power remaining on a tablet x hours after it is turned on. Which device stays on longer?
The tablet stays on longer
The variable that represents the input values of a function
Independent Variable
Let c(t) be the number of customers in a restaurant t hours after 8 AM
a. c(0)=0
b. c(3)=c(8)
b. There are the same number of customers at 11 AM as there are at 4 PM
An event center charges $59.95 for each concert ticket
A. Does this situation represent a function? If so, identify the independent and dependent variables
B. There are 9350 seats in the arena. Find the domain and range. Is the domain discrete or continuous?
A. Yes: Profit is the dependent variable, and the number of tickets sold is the independent variable
B. domain: the set of integers between 0 and 9350; range: 0 less than or equal to p less than or equal to 560,532.50; discrete; you cannot buy part of a ticket
The table shows your earnings y (in dollars) for working x hours. You work no more than 18 hours each week.
x
time (hours)_4_5_6_7
earning (in dollars)_40.80_51_61.20_71.40
A. What is your hourly pay rate?
B. Find the domain and range of the function.
A.$10.20
Domain: 0 is less than or equal to x is less than or equal to 18
Range: 0 is less than or equal to y is less than or equal to 183.60
You order 2 hamburgers and a drink. The drink costs $1.50. You pay a total of $5.83 including a sales tax of 6%. How much did ONE burger cost.
$1.99
A pairing of inputs with outputs
Relations