# Common Core: High School - Functions : Combining Standard Function Types by Arithmetic Operations: CCSS.Math.Content.HSF-BF.A.1b

## Example Questions

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### Example Question #21 : Building Functions

Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every  days and can be modeled by a function  which depends on  days. Before the fertilizer is added to the pot, Janet had seven blooms. Write a function that models the number of blooms in  days since the fertilizer was added.

Explanation:

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.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 what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is seven.

The fertilizer produces four blooms every two days. If  is representing days then the rate of the blooms is,

.

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.

### Example Question #12 : Combining Standard Function Types By Arithmetic Operations: Ccss.Math.Content.Hsf Bf.A.1b

Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every  days and can be modeled by a function  which depends on  days. Before the fertilizer is added to the pot, Janet had fifteen blooms. Write a function that models the number of blooms in  days since the fertilizer was added.

Explanation:

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.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 what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is fifteen.

The fertilizer produces four blooms every two days. If  is representing days then the rate of the blooms is,

.

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.

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