### All Algebra 1 Resources

## Example Questions

### Example Question #1 : Algebraic Functions

A function is given by . Find .

**Possible Answers:**

**Correct answer:**

Plugging in 2 wherever is present in the formula yields an answer of 14.

### Example Question #2 : Algebraic Functions

If , evaluate .

**Possible Answers:**

**Correct answer:**

To solve this function, we simply need to understand that finding means that in this specific case. So, we can just substitute 10 in for .

is equal to , so our final answer is

or .

### Example Question #3 : Algebraic Functions

In which of these relations is *not* a function of ?

**Possible Answers:**

**Correct answer:**

In the relation , there are many values of that can be paired with more than one value of - for example, .

To demonstrate that is a function of in the other examples, we solve each for :

can be rewritten as .

can be rewritten as

can be rewritten as

need not be rewritten.

In each case, we see that for any value of , can be uniquely defined.

### Example Question #1 : How To Find F(X)

**Possible Answers:**

**Correct answer:**

### Example Question #2 : How To Find F(X)

What is the next number in the following sequence?

**Possible Answers:**

**Correct answer:**

To form this sequence, alternately multiply by 2 and add 5:

To keep the pattern going, double the seventh term to get the eighth:

### Example Question #6 : Algebraic Functions

Define and

Evaluate

**Possible Answers:**

is undefined.

**Correct answer:**

The easiest way to find is to take advantage of the fact that the radical expressons are conjugates, and that their product follows the difference of squares pattern.

### Example Question #3 : How To Find F(X)

Define and .

Evaluate

**Possible Answers:**

is undefined.

**Correct answer:**

is undefined.

The domain of is the intersection of the domains of the functions and . Both domains are restricted by the same radical expression; since it must hold that the common radicand is positive:

or

is therefore outside of the domains of and and, subsequently, that of .

### Example Question #4 : How To Find F(X)

What is the next number in the following sequence:

**Possible Answers:**

**Correct answer:**

To get each member of this sequence, add a number that increases by one with each element:

To get the next element, add 7:

### Example Question #5 : How To Find F(X)

If , then what is ?

**Possible Answers:**

**Correct answer:**

Replace with in the definition, then simplify.

### Example Question #6 : How To Find F(X)

If , then what is ?

**Possible Answers:**

**Correct answer:**

Replace with in the definition, then simplify.

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