Function or Not?
Rate of Change and Initial Value
Comparing Functions
Linear vs Nonlinear
100
Is the following a function?
NOT a function.
It does not pass the vertical line test.
100
Jamie is selling candles and has graphed her supply below. How many candles did Jamie start off with initially?
Jamie started off with 100 candles. At time 0, she had 100.
100
Which function has a greater initial value?
Function A
Function B
y= = 3x - 3
Function A. Function A's initial value would be 20. Function B's initial value would be -3. 20>-3
100
Is the function linear or non-linear?
Linear
200
Is the following a function?
{(3, 5) (5, 8) (2, 7) (3, 4)}
No, it is not a function.
x-value of 3 is repeated.
200
Jamie is selling candles and has graphed her supply below. What rate shows Jamie's candle supply with respect to time?
Rate = -20.
Down 20 over 1.
200
Allen is driving home at 45 mph. He is currently 160 miles from home. James is also driving home and his distance from home and time can be seen in the table below. Who is traveling at a faster rate?
James Driving Home
James. James is going 50mph, Allen is going 45mph.
200
Is the function Linear or Non-Linear?
6x^3-y=5
Nonlinear.
The exponent makes the function non-linear.
300
Is the equation y = x a function?
Yes, It would pass the vertical line test.
300
George buys and sells Pokemon cards. He currently has 50 and each week he sells 10 Ninja Turtles and buys 6 more. What is George's rate of change for his Pokemon card supply?
His rate is -4 per week. Each week his supply would decrease by 4 (sell 10-->buy 6-->4 more sold then bought).
300
How many times bigger is the rate of Function A than the rate of Function B?
Function A
y=9/5x +12
Function B
1.2 times bigger. Function A has a rate of 9/5=1.8. Function B has a rate of 3/2=1.5.
1.8/1.5=1.2
300
Is the following function linear or non-linear?
Nonlinear. The rate of change is not the same anywhere.
400
Mark has the table below. If the inputs and outputs were switched (meaning the x values are now y and vice versa) would the relation be a function?
No it would not be a function. The new x-value of 13 has 2 different y-values 8 and 9.
400
James has 25 bananas and is picking 4 more bananas every 5 minutes. How many bananas is James picking per minute?
James is picking at a rate of 4/5=0.8 bananas every minute.
400
Anthony is parking cars and the number of cars he's parked can be represented by the equation y=12x + 35 where x is the number of hours he is working and y is the total cars parked. Tyler is also parking cars and the number of cars he parked can be seen in the graph below. How many more cars would Anthony park in 4 hours than Tyler?
Anthony would have parked 3 more cars than Tyler. Using Anthony's equation y=12(4) + 35 = 83 cars parked. Tylers equation y=15(4) + 20 = 80.
400
A runner runs a race at a constant pace - never slowing down, speed up, or stopping. Would this be an example of a linear function?
Yes, it is linear because the rate of change is constant throughout the entire race.