2
College Algebra
Milestone 5 - All Answers
!!!.
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
•
,2
•
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.
,2
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
, 2
3 $5,202.00
4 $5,306.04
5 $5,412.16
College Algebra
Milestone 5 - All Answers
!!!.
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
•
,2
•
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.
,2
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
, 2
3 $5,202.00
4 $5,306.04
5 $5,412.16
