All Common Core: High School - Functions Resources
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
?
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
Step 4: Answer the question.
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
?
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
?
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 #51 : Linear, Quadratic, & Exponential Models*
Which value for proves that the function
will increases faster than the function
?
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
Step 4: Answer the question.
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
?
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
Step 4: Answer the question.
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
?
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
Step 4: Answer the question.
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
?
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
Step 4: Answer the question.
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
?
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
Step 4: Answer the question.
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
?
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
Step 4: Answer the question.
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
?
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
Step 4: Answer the question.
For values ,
.
All Common Core: High School - Functions Resources
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