### All Common Core: High School - Functions Resources

## Example Questions

### Example Question #1 : Linear, Quadratic, & Exponential Models*

Determine whether the situations below are described as linear or exponential functions.

Tina's allowance increases every month.

Johnny is years older than Jane.

**Possible Answers:**

Tina's allowance increases every month is a linear function.

Johnny is years older than Jane is an exponential function.

Tina's allowance increases every month is linear function.

Johnny is years older than Jane is a linear function.

Tina's allowance increases every month is an exponential function.

Johnny is years older than Jane is an exponential function.

Tina's allowance increases every month is an exponential function.

Johnny is years older than Jane is a linear function.

More information is needed.

**Correct answer:**

Tina's allowance increases every month is an exponential function.

Johnny is years older than Jane is a linear function.

This question is testing one's ability to identify and prove whether situations and their functions are linear or exponential. The key concept in questions like these, is understanding and recognizing that linear functions grow by equal differences over intervals, where as exponential functions grow by equal factors over intervals.

For the purpose of Common Core Standards, proving that linear functions grow by difference and exponential functions grow by factors, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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: Examine the first statement.

I. Identify if it is increase/decreasing by a constant or by a percentage that is dependent on another value in the statement.

Statement one: Tina's allowance increases every month. In this particular case the amount of increase depends on the monthly allowance. In other words as the monthly allowance increases the increase becomes a greater dollar amount as time increases. Therefore, the increase is by a percentage.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a percentage, statement one is an exponential function.

Step 2: Examine the second statement.

I. Identify if it is increase/decreasing by a constant or by a percentage that is dependent on another value in the statement.

Statement two: Johnny is years older than Jane. In this particular case Johnny's age can be written as a function of Jane's age. Since Johnny is years older than Jane this is a constant difference. In other words, as the years go on, Johnny's age increase but so does Jane's therefore, Johnny remains years older than Jane across all time intervals.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a constant, statement two is a linear function.

Step 3: Answer the question.

Tina's allowance increases every month is an exponential function.

Johnny is years older than Jane is a linear function.

Recall that for a statement to be linear it must show growth of a constant difference. This means that the output has the same difference for each one increase to the input value. For a statement to be exponential, it must show growth by a common factor.

### Example Question #2 : Linear, Quadratic, & Exponential Models*

Determine whether the situation describes a linear or exponential function.

Tina's allowance increases by every month.

**Possible Answers:**

Tina's allowance increases by every month is an exponential function.

More information is needed.

Tina's allowance increases by every month is neither a linear nor an exponential function.

Tina's allowance increases by every month is a both a linear and exponential function.

Tina's allowance increases by every month is a linear function.

**Correct answer:**

Tina's allowance increases by every month is a linear function.

This question is testing one's ability to identify and prove whether situations and their functions are linear or exponential. The key concept in questions like these, is understanding and recognizing that linear functions grow by equal differences over intervals, where as exponential functions grow by equal factors over intervals.

For the purpose of Common Core Standards, proving that linear functions grow by difference and exponential functions grow by factors, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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: Examine the statement.

I. Identify if it is increase/decreasing by a constant or by a percentage that is dependent on another value in the statement.

Statement: Tina's allowance increases by every month. In this particular case the amount of increases by a constant of two dollars every month.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a constant, the statement is a linear function.

Step 3: Answer the question.

Tina's allowance increases by every month is a linear function.

Recall that for a statement to be linear it must show growth of a constant difference. This means that the output has the same difference for each one increase to the input value. For a statement to be exponential, it must show growth by a common factor.

### Example Question #3 : Linear, Quadratic, & Exponential Models*

Determine whether the situation describes a linear or exponential function.

Tina's allowance increases every month.

**Possible Answers:**

Tina's allowance increases every month is both an exponential and linear function.

Tina's allowance increases every month is neither an exponential nor a linear function.

Tina's allowance increases every month is an exponential function.

More information is needed.

Tina's allowance increases every month is a linear function.

**Correct answer:**

Tina's allowance increases every month is an exponential function.

This question is testing one's ability to identify and prove whether situations and their functions are linear or exponential. The key concept in questions like these, is understanding and recognizing that linear functions grow by equal differences over intervals, where as exponential functions grow by equal factors over intervals.

For the purpose of Common Core Standards, proving that linear functions grow by difference and exponential functions grow by factors, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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: Examine the statement.

Statement: Tina's allowance increases every month. In this particular case the amount of increase depends on the monthly allowance. In other words as the monthly allowance increases the increase becomes a greater dollar amount as time increases. Therefore, the increase is by a percentage.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a percentage, statement one is an exponential function.

Step 3: Answer the question.

Tina's allowance increases every month is an exponential function.

Recall that for a statement to be linear it must show growth of a constant difference. This means that the output has the same difference for each one increase to the input value. For a statement to be exponential, it must show growth by a common factor.

### Example Question #4 : Linear, Quadratic, & Exponential Models*

Determine whether the situation describes a linear or exponential function.

Johnny is years older than Jane.

**Possible Answers:**

Johnny is years older than Jane is neither a linear nor an exponential function.

More information is needed.

Johnny is years older than Jane is an exponential function.

Johnny is years older than Jane is a linear function.

Johnny is years older than Jane is both a linear and an exponential function.

**Correct answer:**

Johnny is years older than Jane is a linear function.

Step 1: Examine the statement.

Statement: Johnny is years older than Jane. In this particular case Johnny's age can be written as a function of Jane's age. Since Johnny is years older than Jane this is a constant difference. In other words, as the years go on, Johnny's age increase but so does Jane's therefore, Johnny remains years older than Jane across all time intervals.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a constant, statement two is a linear function.

Step 3: Answer the question.

Johnny is years older than Jane is a linear function.

### Example Question #5 : Linear, Quadratic, & Exponential Models*

Determine whether the situation describes a linear or exponential function.

Johnny is years older than Jane.

**Possible Answers:**

Johnny is years older than Jane is a linear function.

Johnny is years older than Jane is neither a linear nor exponential function.

More information is needed

Johnny is years older than Jane is both a linear and an exponential function.

Johnny is years older than Jane is an exponential function.

**Correct answer:**

Johnny is years older than Jane is a linear function.

Step 1: Examine the statement.

Statement: Johnny is years older than Jane. In this particular case Johnny's age can be written as a function of Jane's age. Since Johnny is years older than Jane this is a constant difference. In other words, as the years go on, Johnny's age increase but so does Jane's therefore, Johnny remains years older than Jane across all time intervals.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a constant, statement two is a linear function.

Step 3: Answer the question.

Johnny is years older than Jane is a linear function.

### Example Question #6 : Linear, Quadratic, & Exponential Models*

Determine whether the situation describes a linear or exponential function.

Tina's allowance increases every month.

**Possible Answers:**

Tina's allowance increases every month is a linear function.

Tina's allowance increases every month is both an exponential and linear function.

Tina's allowance increases every month is neither an exponential nor linear function.

Tina's allowance increases every month is an exponential function.

More information is needed.

**Correct answer:**

Tina's allowance increases every month is an exponential function.

Step 1: Examine the statement.

Statement: Tina's allowance increases every month. In this particular case the amount of increase depends on the monthly allowance. In other words as the monthly allowance increases the increase becomes a greater dollar amount as time increases. Therefore, the increase is by a percentage.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a percentage, statement one is an exponential function.

Step 3: Answer the question.

Tina's allowance increases every month is an exponential function.

### Example Question #7 : Linear, Quadratic, & Exponential Models*

Determine whether the situation describes a linear or exponential function.

Tina's allowance increases every month.

**Possible Answers:**

Tina's allowance increases every month is both an exponential and linear function.

Tina's allowance increases every month is an exponential function.

Tina's allowance increases every month is a linear function.

Tina's allowance increases every month is neither an exponential nor linear function.

More information is needed.

**Correct answer:**

Tina's allowance increases every month is an exponential function.

Step 1: Examine the statement.

Statement: Tina's allowance increases every month. In this particular case the amount of increase depends on the monthly allowance. In other words as the monthly allowance increases the increase becomes a greater dollar amount as time increases. Therefore, the increase is by a percentage.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a percentage, statement one is an exponential function.

Step 3: Answer the question.

Tina's allowance increases every month is an exponential function.

### Example Question #8 : Linear, Quadratic, & Exponential Models*

Determine whether the situation describes a linear or exponential function.

Johnny is years older than Jane.

**Possible Answers:**

Johnny is years older than Jane is both a linear and exponential function.

Johnny is years older than Jane is a linear function.

Johnny is years older than Jane is an exponential function.

Johnny is years older than Jane is neither a linear nor exponential function.

More information is needed.

**Correct answer:**

Johnny is years older than Jane is a linear function.

Step 1: Examine the statement.

Statement: Johnny is years older than Jane. In this particular case Johnny's age can be written as a function of Jane's age. Since Johnny is years older than Jane this is a constant difference. In other words, as the years go on, Johnny's age increase but so does Jane's therefore, Johnny remains years older than Jane across all time intervals.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a constant, statement two is a linear function.

Step 3: Answer the question.

Johnny is years older than Jane is a linear function.

### Example Question #9 : Linear, Quadratic, & Exponential Models*

Determine whether the situation describes a linear or exponential function.

Tina's allowance increases by every month.

**Possible Answers:**

More information is needed.

Tina's allowance increases by every month is a linear function.

Tina's allowance increases by every month is an exponential function.

Tina's allowance increases by every month is neither a linear nor exponential function.

Tina's allowance increases by every month is both a linear and exponential function.

**Correct answer:**

Tina's allowance increases by every month is a linear function.

Step 1: Examine the statement.

Statement: Tina's allowance increases by every month. In this particular case the amount of increases by a constant of every month.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a constant, the statement is a linear function.

Step 3: Answer the question.

Tina's allowance increases by every month is a linear function.

### Example Question #10 : Linear, Quadratic, & Exponential Models*

Determine whether the situation describes a linear or exponential function.

Tina's allowance increases by every month.

**Possible Answers:**

Tina's allowance increases by every month is an exponential function.

Tina's allowance increases by every month is both a linear and exponential function.

More information is needed.

Tina's allowance increases by every month is neither a linear nor exponential function.

Tina's allowance increases by every month is a linear function.

**Correct answer:**

Tina's allowance increases by every month is a linear function.

Step 1: Examine the statement.

Statement: Tina's allowance increases by every month. In this particular case the amount of increases by a constant of every month.

II. Conclude whether the statement is linear or exponential.

Since the increase is by a constant, the statement is a linear function.

Step 3: Answer the question.

Tina's allowance increases by every month is a linear function.

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