Select The Correct Texts In The Table.Consider Function { F $} : : : [ f(x) = \left{ \begin{array}{ll} -\frac{1}{4} X^2 + 6x + 36, & X \ \textless \ -2 \ 4x - 15, & -2 \leq X \ \textless \ 4 \ 3^{x-4}, & X \ \textgreater \

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Introduction

In this article, we will delve into the world of mathematics and explore a function { f $}$ defined by a piecewise function. The function { f $}$ is given by:

f(x)={−14x2+6x+36,x \textless −24x−15,−2≤x \textless 43x−4,x \textgreater { f(x) = \left\{ \begin{array}{ll} -\frac{1}{4} x^2 + 6x + 36, & x \ \textless \ -2 \\ 4x - 15, & -2 \leq x \ \textless \ 4 \\ 3^{x-4}, & x \ \textgreater \ \end{array} \right. }

We will analyze the function and determine the correct texts in the table based on the given conditions.

Understanding the Function

The function { f $}$ is a piecewise function, which means it is defined by multiple sub-functions, each applicable to a specific interval of the domain. The function has three sub-functions:

  1. For x < -2: The function is defined as −14x2+6x+36{-\frac{1}{4} x^2 + 6x + 36}.
  2. For -2 ≤ x < 4: The function is defined as 4x−15{4x - 15}.
  3. For x > 4: The function is defined as 3x−4{3^{x-4}}.

Analyzing the Conditions

To determine the correct texts in the table, we need to analyze the conditions given in the problem. The conditions are:

  • x < -2: The function is defined as −14x2+6x+36{-\frac{1}{4} x^2 + 6x + 36}.
  • -2 ≤ x < 4: The function is defined as 4x−15{4x - 15}.
  • x > 4: The function is defined as 3x−4{3^{x-4}}.

Determining the Correct Texts

Based on the conditions, we can determine the correct texts in the table as follows:

Interval Function
x < -2 −14x2+6x+36{-\frac{1}{4} x^2 + 6x + 36}
-2 ≤ x < 4 4x−15{4x - 15}
x > 4 3x−4{3^{x-4}}

Conclusion

In conclusion, the correct texts in the table are determined based on the conditions given in the problem. The function { f $}$ is a piecewise function, and each sub-function is applicable to a specific interval of the domain. By analyzing the conditions, we can determine the correct texts in the table.

Example Use Cases

The function { f $}$ has several example use cases, including:

  • Finding the value of the function at a specific point: We can use the function to find the value of the function at a specific point, such as x = -3 or x = 5.
  • Graphing the function: We can use the function to graph the function and visualize its behavior.
  • Solving equations involving the function: We can use the function to solve equations involving the function, such as finding the values of x that satisfy the equation f(x) = 0.

Step-by-Step Solution

To solve the problem, follow these steps:

  1. Read the problem carefully: Read the problem carefully and understand the conditions given.
  2. Determine the correct interval: Determine the correct interval based on the conditions given.
  3. Choose the correct function: Choose the correct function based on the interval determined.
  4. Write the correct text: Write the correct text in the table based on the function chosen.

Tips and Tricks

  • Pay attention to the conditions: Pay attention to the conditions given in the problem and make sure to choose the correct interval and function.
  • Use the correct notation: Use the correct notation when writing the function, such as using parentheses to group terms.
  • Check your work: Check your work to make sure that you have chosen the correct interval and function.

Common Mistakes

  • Choosing the wrong interval: Choosing the wrong interval can lead to incorrect results.
  • Choosing the wrong function: Choosing the wrong function can lead to incorrect results.
  • Not paying attention to the conditions: Not paying attention to the conditions can lead to incorrect results.

Conclusion

Frequently Asked Questions

In this article, we will answer some frequently asked questions related to selecting the correct texts in the table based on the function { f $}$.

Q: What is the function { f $}$ defined by?

A: The function { f $}$ is defined by a piecewise function, which means it is defined by multiple sub-functions, each applicable to a specific interval of the domain.

Q: What are the three sub-functions of the function { f $}$?

A: The three sub-functions of the function { f $}$ are:

  1. For x < -2: The function is defined as −14x2+6x+36{-\frac{1}{4} x^2 + 6x + 36}.
  2. For -2 ≤ x < 4: The function is defined as 4x−15{4x - 15}.
  3. For x > 4: The function is defined as 3x−4{3^{x-4}}.

Q: How do I determine the correct interval based on the conditions given?

A: To determine the correct interval based on the conditions given, you need to analyze the conditions and choose the interval that satisfies the condition.

Q: How do I choose the correct function based on the interval determined?

A: To choose the correct function based on the interval determined, you need to look at the sub-functions defined for each interval and choose the function that corresponds to the interval.

Q: What are some common mistakes to avoid when selecting the correct texts in the table?

A: Some common mistakes to avoid when selecting the correct texts in the table include:

  • Choosing the wrong interval: Choosing the wrong interval can lead to incorrect results.
  • Choosing the wrong function: Choosing the wrong function can lead to incorrect results.
  • Not paying attention to the conditions: Not paying attention to the conditions can lead to incorrect results.

Q: How do I check my work to make sure that I have chosen the correct interval and function?

A: To check your work, you can:

  • Re-read the problem: Re-read the problem to make sure that you understand the conditions given.
  • Double-check your interval: Double-check your interval to make sure that it is correct.
  • Double-check your function: Double-check your function to make sure that it is correct.

Q: What are some example use cases of the function { f $}$?

A: Some example use cases of the function { f $}$ include:

  • Finding the value of the function at a specific point: We can use the function to find the value of the function at a specific point, such as x = -3 or x = 5.
  • Graphing the function: We can use the function to graph the function and visualize its behavior.
  • Solving equations involving the function: We can use the function to solve equations involving the function, such as finding the values of x that satisfy the equation f(x) = 0.

Q: How do I graph the function { f $}$?

A: To graph the function { f $}$, you can:

  • Use a graphing calculator: Use a graphing calculator to graph the function.
  • Use a graphing software: Use a graphing software to graph the function.
  • Plot the function by hand: Plot the function by hand using a coordinate plane.

Q: How do I solve equations involving the function { f $}$?

A: To solve equations involving the function { f $}$, you can:

  • Use algebraic methods: Use algebraic methods to solve the equation.
  • Use numerical methods: Use numerical methods to solve the equation.
  • Use a graphing calculator: Use a graphing calculator to solve the equation.

Conclusion

In conclusion, selecting the correct texts in the table based on the function { f $}$ requires careful analysis of the conditions given and choosing the correct interval and function. By following the steps outlined in this article, you can determine the correct texts in the table and use the function to solve equations and graph the function.