All Common Core: High School - Functions Resources
Example Questions
Example Question #1 : Invertible And Non Invertible Functions: Ccss.Math.Content.Hsf Bf.B.4d
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
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: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
The inverse graphed alone is as follows.
Example Question #2 : Invertible And Non Invertible Functions: Ccss.Math.Content.Hsf Bf.B.4d
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
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: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically
.
Example Question #3 : Invertible And Non Invertible Functions: Ccss.Math.Content.Hsf Bf.B.4d
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
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: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
.
Example Question #4 : Invertible And Non Invertible Functions: Ccss.Math.Content.Hsf Bf.B.4d
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
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: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Example Question #5 : Invertible And Non Invertible Functions: Ccss.Math.Content.Hsf Bf.B.4d
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
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: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Example Question #6 : Invertible And Non Invertible Functions: Ccss.Math.Content.Hsf Bf.B.4d
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
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: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Example Question #7 : Invertible And Non Invertible Functions: Ccss.Math.Content.Hsf Bf.B.4d
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
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: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Example Question #1 : Invertible And Non Invertible Functions: Ccss.Math.Content.Hsf Bf.B.4d
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
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: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Example Question #9 : Invertible And Non Invertible Functions: Ccss.Math.Content.Hsf Bf.B.4d
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
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: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Example Question #10 : Invertible And Non Invertible Functions: Ccss.Math.Content.Hsf Bf.B.4d
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
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: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
All Common Core: High School - Functions Resources
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)