Function Notation
Functions
The graph on the left is a function. Function always has only 1 "Y" value for each "X" value. Also the graph would have to pass the vertical line test which means you get a straight line and move it across the graph vertically, and that line would always only touch 1 point on the line no matter what.
Like I explained above, each "x" value should only have 1 "y" value to be a function.
*2 differnet x values can have the same Y values, but still be a function.
*2 differnet x values can have the same Y values, but still be a function.
Not a function
The graph shown on the left is not a function. Like I explained before, to be a function, the graph should pass the vertical line test and each "x" value should only have 1 "y" value, but the graph on the left has 2.
The chart on the right is another example of what's not a function. One of the x-values, 5, has 2 y-values to it, 2 AND 9, so this would not be a function.
Example of a Linear Function
Max went to the gas station and saw that the gas price is $3 per gallon. Use function notation to write an equation to see how much x gallons cost.
Answer
G(x)=3x
G(x) stands for the total cost for x gallons.
x represents the number of gallons that Max buys.
The "3" shows that each gallon of gas cost $3.
Answer
G(x)=3x
G(x) stands for the total cost for x gallons.
x represents the number of gallons that Max buys.
The "3" shows that each gallon of gas cost $3.
Let's say that max buys 12 gallons of gas. How much would his total be?
Answer
You would ave to replace x with 12 to find out the total cost.
G(12)=3X12
G(12)=36
So his total would be $36.
Answer
You would ave to replace x with 12 to find out the total cost.
G(12)=3X12
G(12)=36
So his total would be $36.
Example of an Exponential Function
Max has a bank account with a 5% annual growing rate and he starts off with $10000 in his account. Use function notation to write an equation to see how much money he will have in x years.
Answer
f(x)=10000(1.05)^x
f(x) stands for the money in his account after x years.
x represents the number of years he leaves his account.
The 10000 shows the starting point or how much money he has in the beginning.
The 1.05 shows his growing rate. The ammount he has in the beggining grows by adding 5% (the 0.5) with itslf thats already there (1).
Answer
f(x)=10000(1.05)^x
f(x) stands for the money in his account after x years.
x represents the number of years he leaves his account.
The 10000 shows the starting point or how much money he has in the beginning.
The 1.05 shows his growing rate. The ammount he has in the beggining grows by adding 5% (the 0.5) with itslf thats already there (1).
Lets say he visits his account after 20 years. How much money will he have then?
Answer
You would ave to replace x with 20 to find out how much money is in the account.
f(20)=10000(1.05)^20
f(20)=10000*2.65329770514
f(20)=26532.98
So in 20 years, he would have $26532.98 in his account now.
Answer
You would ave to replace x with 20 to find out how much money is in the account.
f(20)=10000(1.05)^20
f(20)=10000*2.65329770514
f(20)=26532.98
So in 20 years, he would have $26532.98 in his account now.