Functions
Linear Functions
Linear or Non-Linear Functions
Writing Linear Equations
Miscellaneous
100
What is a function?
Each input is assigned exactly one output.
100
What is the equation of this linear function?
It is y = (-1/3)x + 5
100
Does this graph represent a linear function?
Yes, it's a linear function!
100
In a linear equation, which variable represents rate of change?
The variable m.
100
Is (3,2) a solution to the system:
2x + 4y = 14
x - y = 2
No
200
Does this table represent a function?
Yes, it's a function!
200
What is the equation of this linear function?
It is y = 4x + 6.
200
No, it's a non-linear function!
200
An online clothing company sells custom sweatshirts. The company charges $6.50 for each sweatshirt and a flat fee of $3.99 for shipping. What linear equation represents this situation?
The linear equation is y = 6.5x + 3.99.
200
Simplify:
3m^2n^3 xx 2m^4n
6m^6n^4
300
Does this graph represent a function?
Yes, it's a function!
300
What test is used to determine if a graph is a function or not?
The Vertical Line Test
300
Without a graph, how do you determine if a function is linear or non-linear?
Calculate rate of change (or slope).
300
Tara wants to rent a tent for an outdoor celebration. One company charges a $100 set-up fee and $350 per hour to rent their tent. What is the linear equation that represents this situation?
The linear equation is y = 350x + 100.
300
Solve:
x - 3y = 6
2x - y = 2
(0,-2)
400
Does this mapping (arrow) diagram represent a function?
Yes, it's a function!
400
Which linear function has the greater rate of change? What is the rate of change for each panda?
The table has a greater rate of change. Mochi has a rate of change of 4 lbs/week. Kappa has a rate of change of 3 lbs/week.
400
Does this table represent a linear function?
No, it's a non-linear function!
400
Write a system of equations:
Jackson bought 3 cokes and 4 hotdogs for 12 dollars and Norma bought 1 coke and 2 hotdogs for 5 dollars.
3c + 4h = 12
1c + 2h = 5
400
Simplify:
(a^4b^3)^2/(a^2b^5)
a^6b
500
(-1, 3), (0, 2), (1, 1), (2, 0), (0, 3)
Does this set of ordered pairs represent a function?
No, it's not a function!
500
Which linear function has a greater initial value? What is the initial value for each panda?
The graph has a greater initial value. Mochi has an initial value of 1 lb. Kappa has an initial value of 2 lbs.
500
Does this table represent a linear function?
Yes, it's a linear function!
500
A store sales packages of comic books with a poster. One package containing 6 comics (and a poster) costs $12.75. Another package containing 13 comics (and a poster) costs $19.75. What is the linear equation that represents this situation? Interpret the rate of change and the initial value.
The linear equation is y = x + 6.75. The rate of change means that each comic costs $1.00. The initial value means that the poster included in each package costs $6.75.
500
Solve the equation:
1/2(4x - 2) - 4 = 3x - 5
x = 0