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Functions
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Definitions and Notations
100
For graph 1: f(-1)?
0
100
For the line y = 2x - 3 what is the y-intercept?
(0,-3)
100
Look at graph 2. What is the solution to the system?
(2,1)
100
Identify the slope in the statement: Amy started a savings account in 1990. She started with $5. She added $500 a year. Include units.
$500/ year.
100
f(7) = 6 means what ordered pair is on the graph?
(7,6)
200
For graph 1. For what x is f(x) = 2
x = -4
200
For the line y = 2x - 3 what is the slope?
m = 2
200
Solve the system 2x + y = 5 3x - 2y = 15 by substitution.
Equation 1 --> y = 5 - 2x Substituting gives 3x - 2(5 - 2x) = 15 Simplifying gives 3x - 10 + 4x = 15 Simplifying gives 7x - 10 = 15 Adding 10 gives 7x = 25 --> x = 25/7 y = 5 - 2(25/7) = -15/7 --> Solution (25/7,-15/7)
200
Identify the y-intercept in the statement: Amy started a savings account in 1990. She started with $5. She added $500 a year.
(0,5) note: It is $5.
200
What is the first step to find the x-intercept?
Set y = 0. Note: Then you solve for x.
300
For graph 1: What is f(2)?
Undefined: Why? The circle is open = NO POINT
300
For the line 3x - 2y = 6, what is the y-intercept?
(0,-3)
300
Solve the system 2x - 3y = 6 2x + 2y = -4 by elimination/ addition.
To eliminate x: Multiply equation 2 by -1 --> -2x -2y = 4 Adding equation 1 to -2x - 2y = 4 gives -5y = 10 --> y = -2 Then 2x - 3(-2) = 6 --> 2x + 6 = 6 Subtracting 6 from both sides --> 2x = 0 --> x = 0 So the solution is (0,-2)
300
Amy started a savings account in 1990. In 2014 she had $5000 in the account. If x = years since 1990, and f(x) = money in the account, what ordered pair represents the statement "In 2014 she had $5000 in the account"
(24,5000) (years since 1990, money)
300
The ordered pair (5,6) is what in function form?
f(5) = 6
400
For graph 1: What is the domain?
(- infinity, 2) or {x | x < 2}
400
For the line y = 2 - 3x what is the slope?
m = -3
400
Clear the fraction in the system: 1/2x - 1/3 y = 5 1/4x + 2y = 1/2
Equation 1: Multiply by 6 --> 3x-2y = 30 Equation 2: Multiply by 4 --> x + 8y = 2
400
Write a function that represents the amount of money in the account (f(x)) , x years since 1992. Amy saves $500 a year. In 2000 her account had $10,000.
f(x) = 500x + 6,000 Note: The 6,000 is how much money she had when she started the account in 1992
400
What is the slope-intercept form of a line?
y = mx + b
500
For graph 1: What is the range?
(- infinity, 2] or { y | y is less then or equal to 2}
500
For the line 3x - 2y = 6, what is the slope?
m = 3/2
500
Define your variables AND set-up (but do not solve) the system of equations that can be used to solve: You plan to mix a drink that is 6% juice with one that is 80% juice. You would like your mixture to be 40% juice. How much of each drink mix do you need to make 5 gallons of the 40%?
Define variables: x = number of gallons of 6% juice Note 6% = 0.06 y = number of gallons of 80% juice Note 80% = 0.8 System: x + y = 5 0.06x +0.8y = .4(5) or 0.06x + 0.8y = 2 NOTE: There are other types of systems applications. Make sure to be prepared for any/ all.
500
f(x) = -200x + 20,000 represents the money in Amy's savings account x months since she inherited money in January 2010 (which she deposited to start the account) Interpret the meanings of -200 and 20,000 in context of the problem.
-200 is the slope. It represents the change in her account per month. She is withdrawing 200 a month. 20,000 is the y-intercept. It is the initial value of of the account in January 1990 (i.e. the money she inherited)
500
What is the point-slope form of the line?
y-y1 = m(x-x1) Note: the 1 in y1 and x1 should be subscript (small, to the right and bottom)