This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output. 

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form  and the question asks to calculate  we know that the input value is four.

Step 2: Given the function, input the desired  value. 

In step one the input value of four was found. Now substitute 4 in for every  in the function.

Step 3: Verify solution by graphing the function.

To find the function value on a graph go to  and find the y value that lies on the graph at . Looking at the graph above when , .

Recall that , thus verifying the solution found in step 2.

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output. 

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the inside function is in the form  and the question asks to calculate  we know that the input value is two.

After the function value of  is calculated, it will be the input value for .

Step 2: Given the function, input the desired  value. 

In step one the input value of two was found. Now substitute 2 in for every in the function .

Step 3: Substitute the function value of the inside portion into .

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output. 

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form  and the question asks to calculate  we know that the input value is negative five.

Step 2: Given the function, input the desired  value. 

In step one the input value of negative five was found. Now substitute -5 in for every  in the function.

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output. 

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.Math.content.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form  and the question asks to calculate  we know that the input value is three.

Step 2: Given the function, input the desired  value. 

In step one the input value of three was found. Now substitute 3 in for every  in the function.

Step 3: Answer the question.

The answer is

This question is testing ones ability to recognize sequences as functions. 

For the purpose of Common Core Standards, sequences fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the pattern of the given sequence.

For this particular problem, the common difference needs to be calculated as it is an arithmetic sequence.

To identify the pattern or in other words, calculate the common difference, subtract the first term from the second term. Then subtract the second term from the third term. For an arithmetic sequence these two differences should be equal to one another.

Given this particular sequence 

the common difference using the above method is as follows.

Step 2: Find the value of the square.

To find the value of the square add the common difference to the previous term in the sequence.

The term before the square is nine, therefore the value of the square is,

.

The sequence is now,

Step 3: Find the value of the triangle.

To find the value of the triangle add the common difference to the previous term in the sequence.

This question is testing ones ability to recognize sequences as functions. 

For the purpose of Common Core Standards, sequences fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the pattern of the given sequence.

For this particular problem, the common ratio needs to be calculated as it is an geometric sequence.

To identify the pattern or in other words, calculate the common ratio, divide the second term by the first term. Then divide the third term by the second term. For an geometric sequence these two ratios should be equal to one another.

Given this particular sequence 

the common ratio using the above method is as follows.

Step 2: Find the next value.

To find the value of the next term multiply the common ratio to the previous term in the sequence.

The last term is 49, therefore the value of the next term is,

.

The sequence is now,

Step 3: Find the next value.

To find the value of the next term multiply the common ratio to the previous term in the sequence.

Step 4: Answer the question.

The next two terms in the sequence are, .

This question is testing ones ability to recognize sequences as functions and identify specific entry values. 

For the purpose of Common Core Standards, sequences fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the pattern of the given sequence.

Since the sequence starts with the assumed input value of zero and the given sequence values of,

the following logic statement can be created.

Let  represent the sequence value for the input value . In other words,

Looking at the values, the difference between entry two and entry one is two. The difference between entry three and entry two is four. The difference between entry four and entry three is eight. Finally, the difference between entry five and entry four is sixteen. This pattern signifies that the increase between each entry is double the difference of the previous terms.

Step 2: Write the logic statement for the sequence in mathematical terms.

Step 3: Find the function for this particular sequence.

Since the previous term minus the term before it will always equal two, another way to write this sequence is

Step 3: Verify function for known terms.

Step 4: Calculate the specific value in question.

This question is testing ones ability to recognize sequences as functions and identify specific entry values. 

For the purpose of Common Core Standards, sequences fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the pattern of the given sequence.

Looking at the above sequence it is seen that each term is a perfect square. Perfect square are composed of one number being multiplied by itself. In other words, when one takes the square root of a perfect square the value that is found is a factor that when squared results in the perfect square.

In mathematical terms this concept looks like the following.

Step 2: Write the sequence with the identified pattern found in step 1.

Becomes,

.

Step 3: Continuing the pattern, solve for the triangle and square.

Therefore,

Step 4: Answer the question.

This question is testing ones ability to recognize sequences as functions. 

For the purpose of Common Core Standards, sequences fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the pattern of the given sequence.

For this particular problem, the common difference needs to be calculated as it is an arithmetic sequence.

To identify the pattern or in other words, calculate the common difference, subtract the first term from the second term. Then subtract the second term from the third term. For an arithmetic sequence these two differences should be equal to one another.

Given this particular sequence the common difference is calculated as follows.

Therefore, the common difference is negative six. In other words, each term decreases by six every time.

Step 2: Use the common difference to find the missing terms in the sequence.

Step 3: Answer the question.

The sequence becomes,

therefore.

.

This question is testing ones ability to recognize sequences as functions. 

For the purpose of Common Core Standards, sequences fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONENT.HSF-IF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the pattern of the given sequence.

For this particular problem, the common difference needs to be calculated as it is an arithmetic sequence.

To identify the pattern or in other words, calculate the common difference, subtract the first term from the second term. Then subtract the second term from the third term. For an arithmetic sequence these two differences should be equal to one another.

Given this particular sequence 

Therefore, the common difference for this sequence is negative four. In other words, the sequence is decreased by four every time.

Step 2: Calculate the next term in the sequence by adding the common difference to the last term given.