The Function $h(x)$ Is A Transformation Of The Square Root Parent Function, $f(x)=\sqrt{x}$. What Function Is \$h(x)$[/tex\]?A. $h(x)=\sqrt{x-1}$ B. $h(x)=\sqrt{x+1}$ C.

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Introduction

In mathematics, the transformation of functions is a crucial concept that helps us understand how different functions can be obtained from a given parent function. The square root parent function, $f(x)=\sqrt{x}$, is a fundamental function in mathematics that has various applications in different fields. In this article, we will discuss the transformation of the square root parent function and determine the function $h(x)$.

Understanding the Square Root Parent Function

The square root parent function, $f(x)=\sqrt{x}$, is a function that takes a non-negative real number as input and returns its square root. This function is defined for all non-negative real numbers, i.e., $x \geq 0$. The graph of the square root parent function is a curve that starts at the origin (0,0) and increases as x increases.

Transformation of the Square Root Parent Function

A transformation of a function is a new function that is obtained by applying a specific operation to the original function. In the case of the square root parent function, we can apply various transformations to obtain different functions. Some common transformations include:

  • Vertical Stretching: This involves multiplying the function by a constant factor.
  • Vertical Shifting: This involves adding or subtracting a constant value to the function.
  • Horizontal Stretching: This involves multiplying the input of the function by a constant factor.
  • Horizontal Shifting: This involves adding or subtracting a constant value to the input of the function.

Determining the Function $h(x)$

To determine the function $h(x)$, we need to apply a specific transformation to the square root parent function. Let's consider the options given:

A. $h(x)=\sqrt{x-1}$ B. $h(x)=\sqrt{x+1}$ C. $h(x)=\sqrt{x-2}$

We can apply the transformation to each option and determine which one is correct.

Applying the Transformation

Let's apply the transformation to each option:

A. $h(x)=\sqrt{x-1}$

This option involves subtracting 1 from the input of the function. This is a horizontal shifting of the square root parent function by 1 unit to the right.

B. $h(x)=\sqrt{x+1}$

This option involves adding 1 to the input of the function. This is a horizontal shifting of the square root parent function by 1 unit to the left.

C. $h(x)=\sqrt{x-2}$

This option involves subtracting 2 from the input of the function. This is a horizontal shifting of the square root parent function by 2 units to the right.

Conclusion

Based on the transformation applied to each option, we can conclude that the correct function is:

A. $h(x)=\sqrt{x-1}$

This function involves a horizontal shifting of the square root parent function by 1 unit to the right. Therefore, the function $h(x)$ is $h(x)=\sqrt{x-1}$.

Final Answer

The final answer is $h(x)=\sqrt{x-1}$.

Discussion

The transformation of functions is a crucial concept in mathematics that helps us understand how different functions can be obtained from a given parent function. In this article, we discussed the transformation of the square root parent function and determined the function $h(x)$. The correct function is $h(x)=\sqrt{x-1}$, which involves a horizontal shifting of the square root parent function by 1 unit to the right.

References

  • [1] "Functions" by Khan Academy
  • [2] "Transformations of Functions" by Math Open Reference
  • [3] "Square Root Function" by Wolfram MathWorld

Related Articles

  • [1] "The Function Transformation of the Absolute Value Parent Function"
  • [2] "The Function Transformation of the Linear Parent Function"
  • [3] "The Function Transformation of the Quadratic Parent Function"

Tags

  • Function Transformation
  • Square Root Parent Function
  • Horizontal Shifting
  • Mathematics

Introduction

In our previous article, we discussed the transformation of the square root parent function and determined the function $h(x)$. In this article, we will answer some frequently asked questions related to the function transformation of the square root parent function.

Q&A

Q1: What is the square root parent function?

A1: The square root parent function, $f(x)=\sqrt{x}$, is a function that takes a non-negative real number as input and returns its square root.

Q2: What is the transformation of a function?

A2: A transformation of a function is a new function that is obtained by applying a specific operation to the original function. In the case of the square root parent function, we can apply various transformations to obtain different functions.

Q3: What are the common transformations of the square root parent function?

A3: Some common transformations of the square root parent function include:

  • Vertical Stretching: This involves multiplying the function by a constant factor.
  • Vertical Shifting: This involves adding or subtracting a constant value to the function.
  • Horizontal Stretching: This involves multiplying the input of the function by a constant factor.
  • Horizontal Shifting: This involves adding or subtracting a constant value to the input of the function.

Q4: How do you determine the function $h(x)$?

A4: To determine the function $h(x)$, we need to apply a specific transformation to the square root parent function. We can apply the transformation to each option and determine which one is correct.

Q5: What is the correct function $h(x)$?

A5: The correct function $h(x)$ is $h(x)=\sqrt{x-1}$, which involves a horizontal shifting of the square root parent function by 1 unit to the right.

Q6: What is the significance of the function transformation of the square root parent function?

A6: The function transformation of the square root parent function is significant because it helps us understand how different functions can be obtained from a given parent function. This is crucial in mathematics and has various applications in different fields.

Q7: How do you apply the transformation to the square root parent function?

A7: To apply the transformation to the square root parent function, we need to follow these steps:

  1. Identify the type of transformation to be applied (e.g., vertical stretching, vertical shifting, horizontal stretching, or horizontal shifting).
  2. Apply the transformation to the square root parent function.
  3. Determine the new function obtained by the transformation.

Q8: What are the benefits of understanding the function transformation of the square root parent function?

A8: Understanding the function transformation of the square root parent function has several benefits, including:

  • Improved problem-solving skills: By understanding how different functions can be obtained from a given parent function, we can improve our problem-solving skills.
  • Enhanced mathematical knowledge: Understanding the function transformation of the square root parent function enhances our mathematical knowledge and helps us to better understand mathematical concepts.
  • Increased applications: Understanding the function transformation of the square root parent function has various applications in different fields, including science, engineering, and economics.

Conclusion

In this article, we answered some frequently asked questions related to the function transformation of the square root parent function. We discussed the significance of the function transformation of the square root parent function and the benefits of understanding it. We also provided a step-by-step guide on how to apply the transformation to the square root parent function.

Final Answer

The final answer is $h(x)=\sqrt{x-1}$.

Discussion

The function transformation of the square root parent function is a crucial concept in mathematics that helps us understand how different functions can be obtained from a given parent function. In this article, we discussed the significance of the function transformation of the square root parent function and the benefits of understanding it.

References

  • [1] "Functions" by Khan Academy
  • [2] "Transformations of Functions" by Math Open Reference
  • [3] "Square Root Function" by Wolfram MathWorld

Related Articles

  • [1] "The Function Transformation of the Absolute Value Parent Function"
  • [2] "The Function Transformation of the Linear Parent Function"
  • [3] "The Function Transformation of the Quadratic Parent Function"

Tags

  • Function Transformation
  • Square Root Parent Function
  • Horizontal Shifting
  • Mathematics