Functions
Comparing Functions
Linear Functions
Slope & Rate of Change
Solving Equations
100
What is a function?
A relationship where each input has exactly one output.
100
What mathematical value tells you how quickly a linear function changes?
The slope or rate of change.
100
In the equation: y=mx+b
what does (m) represent?
The slope or rate of change.
100
What is the formula for slope between two points?
m = (y_2-y_1)/(x_2-x_1
100
Solve:
x+7=15
x=8
200
Is the following relation a function?
(1,4), (2,7), (3,9), (4,12)
Yes!
200
Which function has the greater rate of change?
y=3x+7 or y=5x+2
y = 5x + 2
the slope is 5
200
In the equation: y=7x+12
what is the initial value?
12
200
Find the slope between: (2,4) and (6,12)
m = (12-4)/(6-2)=8/4=2
200
solve:
3x-5=16
x=7
300
Is the following relation a function?
(1,5), (2,7), (1,9), (3,11)
NO! The input 1 has two different outputs!
300
Function A is represented by: y=4x+10
Function B is represented by the table:
Function A, because its initial value is 10 while Function B's is 5
300
A gym charges a $25 sign-up fee and $15 per month.
Write an equation for the total cost after (m) months.
C = 15m + 25
300
What is the slope of: y=-3x+8
-3
300
Solve:
4(x+3)=28
x=4
400
A function is represented by the table below. What is the rule for the function?
y = 3x + 2
400
Function A has a rate of change of 6 and an initial value of 10.
Function B has a rate of change of 4 and an initial value of 30.
Which function has the greater output when x=15?
Function A:
6(15)+10=100
Function B:
4(15)+30=90
Function A.
400
What does each number represent in the equation? C=8h+35
where (C) is cost and (h) is hours.
8 = cost per hour
35 = initial cost
400
DAILY DOUBLE #1 ⭐ Wager a point value you want to bet for this question!
Find the slope of the line passing through the points (2,7) and (6,19).
m = (19-7)/(6-2)=12/4=3
400
Solve:
3x+8=5x-12
x=10
500
A function has the rule
f(x) = 4x - 7
What is f(6), and explain what the answer represents?
The output is 17 when the input is 6
500
Function A is:
y=3x+50
Function B starts at 10 and increases by 7 for every 1-unit increase in \(x\).
At what value of (x) will the two functions have the same output?
Set equal:
3x+50=7x+10
x=10
500
A water tank contains 800 gallons and loses 25 gallons every minute.
Write an equation for the amount of water after (t) minutes and explain what the slope means.
W = -25t + 800
The slope is −25, meaning the tank loses 25 gallons per minute.
500
Two students calculate the slope of a line passing through (3,5) and (7,13).
Student A:
m=8/4=2
Student B:
m=4/8=1/2
Which student is correct? Explain why.
Student A because student B had the numbers flipped
500
DAILY DOUBLE #2 ⭐. Wager a ppoint value you want to bet for this question.
How many solutions does the following equation have?
4(x+3)=4x+12
Infinitely Many Solutions