SOPHIA 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
•
•
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.
– 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
•
•
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.
