All Algebra II Resources
Example Question #4 : Functions And Graphs
Let and . What is ?
THe notation is a composite function, which means we put the inside function g(x) into the outside function f(x). Essentially, we look at the original expression for f(x) and replace each x with the value of g(x).
The original expression for f(x) is . We will take each x and substitute in the value of g(x), which is 2x-1.
We will now distribute the -2 to the 2x - 1.
We must FOIL the term, because .
Now we collect like terms. Combine the terms with just an x.
The answer is .
Example Question #1 : Function Notation
Solve the function for . When
What does equal when,
Plug 16 in for .
Add 9 to both sides.
Take the square root of both sides. =
Final answer is
Example Question #2 : Understanding Functional Notations
Evaluate if and .
This expression is the same as saying "take the answer of and plug it into ."
First, we need to find . We do this by plugging in for in .
Now we take this answer and plug it into .
We can find the value of by replacing with .
This is our final answer.
Example Question #2 : Function Notation
Orange Taxi company charges passengers a $4.50 base fase, plus $0.10 per mile driven. Write a function to represent the cost of a cab ride, in terms of number of miles driven, .
Total cost of the cab ride is going to equal the base fare ($4.50) plus an additional 10 cents per mile. This means the ride will always start off at $4.50. As the cab drives, the cost will increase by $0.10 each mile. This is represented as $0.10 times the number of miles. Therefore the total cost is:
Example Question #3 : Function Notation
A small office building is to be built with long walls feet long and short walls feet long each. The total length of the walls is to be feet.
Write an equation for in terms of .
The pre-question text provides us with all of the information required to complete this problem.
We know that the total length of the walls is to be ft.
We also know that we have a total of walls and walls.
With this, we can set up an equation and solve for .
Our equation will be with sum of all the walls set equal to the total length of the wall...
Remeber, we want in terms of , which means our equation should look like
Subtract on both sides
Divide by on both sides
Example Question #4 : Function Notation
What is the slope of the function ?
The function is written in slope-intercept form, which means:
= x value
Therefore, the slope is
Example Question #5 : Function Notation
A cable company charges a flat $29.99 activation fee, and an additional $12.99 per month for service. How would a function of the cost be represented in terms of months of service, ?
This cannot be written as a function
The flat rate of 29.99 does not change depending on months of service. It is $29.99 no matter how long services are in use. The monthy fee is directly related to the number of months the services are in use.
Example Question #6 : Function Notation
Find for the following function:
To evaluate , we just plug in a wherever we see an in the function, so our equation becomes
which is equal to
Example Question #7 : Function Notation
Find for the following function:
To find , all we do is plug in wherever we see an in the function. We have to be sure we keep the parentheses. In this case, when we plug in , we get
Then, when we expand our binomial squared and distribute the , we get
Example Question #8 : Function Notation
If , and , for which of the following value(s) will be an odd number?
First, x needs to be plugged into g(x).
Then, the resulting solution needs to be substituted into f(x).
Since 45 is an odd number, 7 is an x value that gives this result. Because both equations subtract an odd number to get the final result, only an odd number will result in an odd result therefore, none of the other options will give an odd result.