# Common Core: High School - Functions : Exponential Functions Exceeding Polynomial Functions: CCSS.Math.Content.HSF-LE.A.3

## Example Questions

### Example Question #1 : Exponential Functions Exceeding Polynomial Functions: Ccss.Math.Content.Hsf Le.A.3

Which value for  proves that the function  will increases faster than the function ?

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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: Use technology to graph .

Step 2: Use technology to graph .

Step 3: Compare the graphs of  and .

Graphically, it appears that  is the point where  increases more rapidly than . Substitute two into both functions to algebraic verify the assumption.

Since

For values .

### Example Question #2 : Exponential Functions Exceeding Polynomial Functions: Ccss.Math.Content.Hsf Le.A.3

Which value for  proves that the function  will increases faster than the function ?

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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: Use technology to graph .

Step 2: Use technology to graph .

Step 3: Compare the graphs of  and .

Graphically, it appears that  is larger than  for all values of .

### Example Question #3 : Exponential Functions Exceeding Polynomial Functions: Ccss.Math.Content.Hsf Le.A.3

Which value for  proves that the function  will increases faster than the function ?

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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: Use technology to graph .

Step 2: Use technology to graph .

Step 3: Compare the graphs of  and .

Graphically, it appears that  is larger than  for all values of .

### Example Question #1 : Exponential Functions Exceeding Polynomial Functions: Ccss.Math.Content.Hsf Le.A.3

Which value for  proves that the function  will increases faster than the function ?

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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: Use technology to graph .

Step 2: Use technology to graph .

Step 3: Compare the graphs of  and .

Graphically, it appears that  is the point where  increases more rapidly than . Substitute this value into both functions to algebraic verify the assumption.

Since

For values .

### Example Question #5 : Exponential Functions Exceeding Polynomial Functions: Ccss.Math.Content.Hsf Le.A.3

Which value for  proves that the function  will increases faster than the function ?

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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: Use technology to graph .

Step 2: Use technology to graph .

Step 3: Compare the graphs of  and .

Graphically, it appears that  is the point where  increases more rapidly than . Substitute this value into both functions to algebraic verify the assumption.

Since

For values .

### Example Question #6 : Exponential Functions Exceeding Polynomial Functions: Ccss.Math.Content.Hsf Le.A.3

Which value for  proves that the function  will increases faster than the function ?

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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: Use technology to graph .

Step 2: Use technology to graph .

Step 3: Compare the graphs of  and .

Graphically, it appears that  is the point where  increases more rapidly than . Substitute this value into both functions to algebraic verify the assumption.

Since

For values .

### Example Question #7 : Exponential Functions Exceeding Polynomial Functions: Ccss.Math.Content.Hsf Le.A.3

Which value for  proves that the function  will increases faster than the function ?

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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: Use technology to graph .

Step 2: Use technology to graph .

Step 3: Compare the graphs of  and .

Graphically, it appears that  is the point where  increases more rapidly than . Substitute this value into both functions to algebraic verify the assumption.

Since

For values .

### Example Question #8 : Exponential Functions Exceeding Polynomial Functions: Ccss.Math.Content.Hsf Le.A.3

Which value for  proves that the function  will increases faster than the function ?

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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: Use technology to graph .

Step 2: Use technology to graph .

Step 3: Compare the graphs of  and .

Graphically, it appears that  is the point where  increases more rapidly than . Substitute this value into both functions to algebraic verify the assumption.

Since

For values .

### Example Question #9 : Exponential Functions Exceeding Polynomial Functions: Ccss.Math.Content.Hsf Le.A.3

Which value for  proves that the function  will increases faster than the function ?

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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: Use technology to graph .

Step 2: Use technology to graph .

Step 3: Compare the graphs of  and .

Graphically, it appears that  is the point where  increases more rapidly than . Substitute this value into both functions to algebraic verify the assumption.

Since

For values .

### Example Question #10 : Exponential Functions Exceeding Polynomial Functions: Ccss.Math.Content.Hsf Le.A.3

Which value for  proves that the function  will increases faster than the function ?

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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: Use technology to graph .

Step 2: Use technology to graph .

Step 3: Compare the graphs of  and .

Graphically, it appears that  is the point where  increases more rapidly than . Substitute this value into both functions to algebraic verify the assumption.

Since