Function Notation
If your wondering just what function notation is, it is just different way of saying "y" . To quickly diagram f(x), the letter before the parentheses names the function, and the letter in the parentheses is the variable being put in the function.
![Picture](/uploads/2/0/0/6/20060679/426847160.jpg)
This Domain and Range table DISPLAYS A FUNCTION because each X-value ONLY HAS ONE Y-value.
![Picture](/uploads/2/0/0/6/20060679/414377908.jpg?269)
This Domain and Range table DOES NOT DISPLAY A FUNCTION because one of the X-values has MORE THAN ONE Y-value.
REAL WORLD SCENARIO
LINEAR
While driving down the road,Jake busted 3 tires in his first car. Then, he took his second car and busted all 4 tires. Tires cost $25 each at GoodeYear in Louisiana. Jake has 5 spare tires at home already. How much money must he spend in all?
Linear Function
t(x)= 25x + 5
This whole scenario is basically about tires. Since it is about tires, we will name the function "t" for tires. The 25 represents the cost of each tire (x). This would be the slope if we were to graph this. The 5 represents how many spare tires he has already. This would represent the y-intercept if we graphed this function.
Evaluate
Looking at the problem, Jake has 7 busted tires. He already 5 spare tires at home which means he will need to buy 2 tires from GoodeYear. To find out the cost, we shall substitute 2 for x.
t(x)= 25x+5
t(2)= 25(2)+5
t(2)= 50+ 5
t(2)= 55
By plugging in two into the function, we figured out that Jake has to pay $55 for the tires.
-Recursive Formula
t1= 30
tn= tn-1 + 25
Exponential
Linear Function
t(x)= 25x + 5
This whole scenario is basically about tires. Since it is about tires, we will name the function "t" for tires. The 25 represents the cost of each tire (x). This would be the slope if we were to graph this. The 5 represents how many spare tires he has already. This would represent the y-intercept if we graphed this function.
Evaluate
Looking at the problem, Jake has 7 busted tires. He already 5 spare tires at home which means he will need to buy 2 tires from GoodeYear. To find out the cost, we shall substitute 2 for x.
t(x)= 25x+5
t(2)= 25(2)+5
t(2)= 50+ 5
t(2)= 55
By plugging in two into the function, we figured out that Jake has to pay $55 for the tires.
-Recursive Formula
t1= 30
tn= tn-1 + 25
Exponential
![Picture](/uploads/2/0/0/6/20060679/548355179.jpg)
Jake decided that he wanted to start recycling plastic bottles. He advertised in the newspaper that he wanted anyone who had unused plastic bottles to send them by the recycling bins in front of his house. At the end of the week, he would have a recycling truck come and empty the bins. The week before he opened the bins, he put in 1 bottle. He started to notice that at the end of every week, the number of plastic bottles doubled. Jake wants to know how many plastic bottles he will have collected on the 15th week.
Exponential Function
r(x)= (1)2^n-1
Since this scenario is about recycling, we will name this function "r". The "1" represents the number of bottles he had on the 0th week. The "2" represents the number of bottles he had on week "1", and the "n-1" represents the end of the week before. Because the number of bottles he has at the end of the week increases exponentially, we use an exponential function to represent the problem.
Evaluate
Jake wants to figure out how many plastic bottles he will have collected at the by the beginning of the 15th week. To evaluate this function, we will substitute "15" into any variable present.
r(x)= (1)2^n-1
r(15)=(1)2^15-1
r(15)=(1)2^14
r(15)=(1)16,384
r(15)=16,384
By plugging in 15, we learned that Jake will have collected 16,384 plastic bottles by the 15th week.
-Recursive Formula
a1= 1
an=(an-1)2
Exponential Function
r(x)= (1)2^n-1
Since this scenario is about recycling, we will name this function "r". The "1" represents the number of bottles he had on the 0th week. The "2" represents the number of bottles he had on week "1", and the "n-1" represents the end of the week before. Because the number of bottles he has at the end of the week increases exponentially, we use an exponential function to represent the problem.
Evaluate
Jake wants to figure out how many plastic bottles he will have collected at the by the beginning of the 15th week. To evaluate this function, we will substitute "15" into any variable present.
r(x)= (1)2^n-1
r(15)=(1)2^15-1
r(15)=(1)2^14
r(15)=(1)16,384
r(15)=16,384
By plugging in 15, we learned that Jake will have collected 16,384 plastic bottles by the 15th week.
-Recursive Formula
a1= 1
an=(an-1)2