College Algebra Milestone 5 - All

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21 questions were answered correctly.

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1

Consider the function .

What are the domain and range of this function?

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RATIONALE

A Square root function has the domain restriction that the

radicand (the value underneath the radical) cannot be

negative. To find the specific domain, construct an

inequality showing that the radicand must be greater than

or equal to zero.

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CONCEPT

Finding the Domain and Range of Functions

2

Kevin examines the following data, which shows the balance in an

investment account.

This tell us that must be greater than or equal to . In

other words, must be less than or equal to . We can

write this inequality in the other direction.

This is the domain of the function, which means all values

must be less than or equal to . To find the range, consider

the fact that it is not possible for the input of the function to

be a negative number.

For all x-values less than or equal to , the function will

have non-negative values for y that only get bigger and

bigger as x increases. The range is all values greater than

or equal to zero.

The expression under the radical, , must be greater

than or equal to zero. To solve this inequality, add to both

sides to undo the subtraction of .

Year Balance

1 $5,000.00

2 $5,100.00

3 $5,202.00

4 $5,306.04

5 $5,412.16

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What is the formula for the geometric sequence represented by

the data above?

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correct

RATIONALE

The first term, which is , so will be replaced by

 in the formula. Next, let's find , the common

ratio.

This is the general formula for a geometric sequence.

We will use information in the table to find values for

and . Let's start with finding , the value of the first

term.

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CONCEPT

Introduction to Geometric Sequences

3

Find the solution for in the equation .

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correct

RATIONALE

This is the formula for the geometric sequence.

To find , take the value of any term, and divide it by the

value of the previous term to find the common ratio. For

example, so . Finally, plug

in values for and into the geometric sequence

formula.

 divided by is equal to . To undo the variable

exponent, apply a logarithm to both sides.

To solve this equation, begin by dividing both sides by

to cancel the coefficient in front of the exponential.

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