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 is 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 raises $570. If the students collect 360 drinks total, how many cans of lemonade and bottles of water were there?
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 (find the solution to the system)?
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)