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?
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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 , sowill 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.
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 , sowill 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.
