Solutions
Solving Systems
Relations vs. Functions
Function Notation
Word Problems
100
Is the ordered pair (-1,2) a solution?
y = 3x + 5
3x+4y=5
YES
100
Solve the following systems of equations
-7x-4y=-4
-9x-y=-30
Solution = (4,-6)
100
A function is a special type of relation where every __________ has exactly one ___________.
input, output (OR x-value, y-value)
100
If f(x) = x - 7, find f(-4).
f(-4) = -11
100
Cass spent $14.85 to buy 13 flowers. She bought lilies, which cost $1.25 and tulips, which cost $0.90 each. How many of each flower did Cass buy?
9 lilies and 4 tulips
200
Is the ordered pair (5, -1) a solution?
x=-2y+3
y=x-4
NO
200
What is the solution of this systems of equations?
y=2x+5
y=3x+9
Solution: (-4,-3)
200
Is the following relation a function?
{(0,1), (2, 3), (3, 2), (0, 4)}
NO, zero repeats in the domain
200
If f(x) = 3x + 9, find f(6).
f(6) = 27
200
Mac joins a fitness club that has a membership fee of $20 plus $15 per month. Uri's club has a fee of $40 and charges $10 per month. Write a systems of equations to represent this situation. DO NOT SOLVE.
y=15x+20
y=10x+40
300
What is the solution of this systems of equations?
Solution = (2,2)
300
Solve the following systems of equations
3x+2y=4
4x+3y=7
Solution= (-2,5)
300
How do we determine if a graph contains a function or not?
Use the vertical line test.
300
If g(x) = x2 + 7x and f(x) = 3x, find f(g(1)).
f(g(1)) = 24
300
The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2 each and bottles of water sell for $1.50 each. The club needs to raise $570 to cover the cost of renting costumes. The students will accept a total of 360 cans and bottles. Write a system of that can be used to represent this situation then solve it.
System:
2x + 1.5y = 570
x + y = 360
Solution: 60 cans of lemonade, 300 bottles of water
400
Solve the following system of equations
y-x-6=0
2y+x=6
Solution: (-2,4)
400
Is the following relation a function?
{(-3, 3), (9, 3), (8, 3), (4, 3)}
YES, none of the x-values repeat
400
If f(x) = x - 1 and g(x) = 2x, find f(g(f(3))).
f(g(f(3))) = 3
400
Taxi company A charges $4 plus $0.50 per mile. Taxi company B charges $5 plus $0.25 per mile. Write a system of equations that could be used to represent this situation. After how many miles will the cost be the same for both taxi cabs?
y=.50x+4
y=0.25x+5
After 4 miles the cost will be the same.
500
Find the value of k so that the system of equations below has no solution:
4x-8y=-4
kx-28y=-13
k = 14
500
Graph the following systems of equations and identify the solution.
y=1/2x+1
y=-3/4x-4
Solution = (-4, -1)
500
Is this equation a function?
y = -4x + 3
YES! (Graph it, then use the Vertical Line Test)