Functions
What letter represents the input of a function?
x
What is the slope of the following function?
y=8x+2
The slope is 8.
William's Spicy Bratwursts come in packs of 5.
How many Bratwursts do you have if you buy 6 packs?
5x6 = 30
Look at this set of ordered pairs:
(2, 6)
(14, 10)
(11, 0)
(14, 15)
Is this relation a function? Why/Why not?
No, it is not. One input (14) has two different outputs (10, 15).
What is the slope of the following function?
7y=35x-28
35/7 = 5
The slope is 5.
Mr. Brocato's healthy savings account gets $150 every week.
How many $ will there be after 7 weeks?
Look at this set of ordered pairs:
(2, 6)
(14, 10)
(11, 0)
(14, 10)
Is this relation a function? Why/Why not?
Yes, it is. Every input has exactly one output.
Find out the slope of the function with the biggest slope:
A. 3y=12x+500
B. 6y=15x-24
C. y=2x
D. 8y=80x+32
A. Slope is 12/3=4
Pizzeria Brocato has just come out with a new pizza: "The Spanish BBQ". Mr. Brocato's professional and extremely qualified pizza makers put exactly 8 slices of bacon for every pizza.
Let p be pizzas and let b be slices of bacon. Write an equation using these variables to represent the relation between pizzas made and slices of bacon used.
p=8b
Does the point (3, 5) satisfy the following equation?:
6y=10x
Yes, it does:
6x5 = 10x3
Mr. Brocato says that: "a nonlinear function MUST ALWAYS have a bigger slope than a linear function".
Draw 2 functions to prove him wrong.
Answers will vary.
Let x be minutes and y be miles.
A motorcycle's path is defined by the following equation: y=2x+2
A car's path is defined by the following equation: y=3x+1
After 4 minutes, what is the distance between the motorcycle and the car?
y=2x4+2 = 10 miles
y=3x4+1 = 13 miles
Distance = 3 miles
Is the following function linear, nonlinear, nonexistent, or impossible?
y=0
Linear.
It is a straight line through the 0.
A line goes through the points (-2, 4) and (3, -6).
Find the slope of the function.
Slope= change(y)/change(x)
Slope= (-6-4)/(3-(-2)) = -10/5 = -2
Mr. Brocato has to go up the WG school stairs every single morning. He decided he would calculate the steepness of the stairs.
He measured that for every 0.3ft that his feet travel forward, his feet travel 0.2ft upwards.
What is the slope of the TERRIBLE stairs?
change (x)=0.3
change (y)=0.2
slope = change(y)/change(x)= 0.2/0.3= 2/3