College Algebra Milestone 5 - All
Answers| Latest Update
You passed this Milestone
21 questions were answered correctly.
1 question was answered incorrectly.
1
Consider the function .
What are the domain and range of this function?
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•
correct
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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.
, 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 .
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.
CONCEPT
Finding the Domain and Range of Functions
2
Kevin examines the following data, which shows the balance in an
investment account.
Year Balance
1 $5,000.00
2 $5,100.00
3 $5,202.00
4 $5,306.04
5 $5,412.16
,What is the formula for the geometric sequence represented by
the data above?
•
•
•
•
correct
RATIONALE
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.
The first term, which is , so will be replaced by
in the formula. Next, let's find , the common
ratio.
, 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.
This is the formula for the geometric sequence.
CONCEPT
Introduction to Geometric Sequences
3
Find the solution for in the equation .
•
•
•
•
correct
RATIONALE
To solve this equation, begin by dividing both sides by
to cancel the coefficient in front of the exponential.
divided by is equal to . To undo the variable
exponent, apply a logarithm to both sides.
Answers| Latest Update
You passed this Milestone
21 questions were answered correctly.
1 question was answered incorrectly.
1
Consider the function .
What are the domain and range of this function?
•
•
correct
•
•
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.
, 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 .
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.
CONCEPT
Finding the Domain and Range of Functions
2
Kevin examines the following data, which shows the balance in an
investment account.
Year Balance
1 $5,000.00
2 $5,100.00
3 $5,202.00
4 $5,306.04
5 $5,412.16
,What is the formula for the geometric sequence represented by
the data above?
•
•
•
•
correct
RATIONALE
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.
The first term, which is , so will be replaced by
in the formula. Next, let's find , the common
ratio.
, 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.
This is the formula for the geometric sequence.
CONCEPT
Introduction to Geometric Sequences
3
Find the solution for in the equation .
•
•
•
•
correct
RATIONALE
To solve this equation, begin by dividing both sides by
to cancel the coefficient in front of the exponential.
divided by is equal to . To undo the variable
exponent, apply a logarithm to both sides.
