### All Algebra II Resources

## Example Questions

### Example Question #1 : Functions And Graphs

Let and . What is ?

**Possible Answers:**

**Correct answer:**

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.

Combine constants.

The answer is .

### Example Question #1 : Function Notation

Solve the function for . When

What does equal when,

**Possible Answers:**

-5

25

0

**Correct answer:**

Plug 16 in for .

Add 9 to both sides.

Take the square root of both sides. =

Final answer is

### Example Question #5 : Understanding Functional Notations

Evaluate if and .

**Possible Answers:**

Undefined

**Correct answer:**

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 #1 : 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, .

**Possible Answers:**

**Correct answer:**

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 #2 : 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 .

**Possible Answers:**

**Correct answer:**

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

something

Subtract on both sides

Divide by on both sides

Simplify

** Answer!!!**

### Example Question #3 : Function Notation

What is the slope of the function ?

**Possible Answers:**

**Correct answer:**

The function is written in slope-intercept form, which means:

where:

= slope

= x value

= y-intercept

Therefore, the slope is

### Example Question #4 : 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, ?

**Possible Answers:**

This cannot be written as a function

**Correct answer:**

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 #5 : Function Notation

Find for the following function:

**Possible Answers:**

**Correct answer:**

To evaluate , we just plug in a wherever we see an in the function, so our equation becomes

which is equal to

### Example Question #6 : Function Notation

Find for the following function:

**Possible Answers:**

**Correct answer:**

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 #7 : Function Notation

If , and , for which of the following value(s) will be an odd number?

**Possible Answers:**

**Correct answer:**

First, x needs to be plugged into g(x).

Then, the resulting solution needs to be substituted into f(x).

For example,

.

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.

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