Complete The Table With The Order Of Operations To Transform F ( X ) = X 2 + 17 F(x) = X^2 + 17 F ( X ) = X 2 + 17 To F ( − 3 X F(-3x F ( − 3 X ].Step | Order Of Operations 1 | Option [ ] 2 | Option [ ]

Introduction

In mathematics, functions are used to describe relationships between variables. Transforming functions involves modifying the original function to create a new one. One common type of transformation is replacing the variable with a multiple of itself. In this article, we will explore how to transform the function $f(x) = x^2 + 17$ to $f(-3x)$ using the order of operations.

Understanding the Order of Operations

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Step 1: Replace the Variable

To transform the function $f(x) = x^2 + 17$ to $f(-3x)$, we need to replace the variable $x$ with $-3x$. This means that every instance of $x$ in the original function will be replaced with $-3x$.

Step	Order of Operations
1	Replace the variable $x$ with $-3x$

Step 2: Apply the Order of Operations

Now that we have replaced the variable, we need to apply the order of operations to simplify the expression.

Step	Order of Operations
2	Evaluate any exponential expressions

In this case, the exponential expression is $(-3x)^2$. Using the order of operations, we evaluate this expression first.

Step 2.1: Evaluate the Exponential Expression

To evaluate the exponential expression $(-3x)^2$, we need to follow the order of operations.

Step	Order of Operations
2.1	Evaluate the expression inside the parentheses

The expression inside the parentheses is $-3x$. We can evaluate this expression by multiplying the coefficient $-3$ by the variable $x$.

Step 2.1.1: Multiply the Coefficient and Variable

Step	Order of Operations
2.1.1	Multiply the coefficient $-3$ by the variable $x$

The result of multiplying the coefficient $-3$ by the variable $x$ is $-3x$.

Step 2.1.2: Square the Result

Step	Order of Operations
2.1.2	Square the result $-3x$

To square the result $-3x$, we need to multiply it by itself.

Step 2.1.2.1: Multiply the Result by Itself

Step	Order of Operations
2.1.2.1	Multiply the result $-3x$ by itself

The result of multiplying the result $-3x$ by itself is $(-3x)^2 = 9x^2$.

Step 2.2: Add the Constant Term

Step	Order of Operations
2.2	Add the constant term $17$

The constant term $17$ is added to the result $9x^2$.

Step 2.2.1: Add the Constant Term to the Result

Step	Order of Operations
2.2.1	Add the constant term $17$ to the result $9x^2$

The result of adding the constant term $17$ to the result $9x^2$ is $9x^2 + 17$.

Step 3: Simplify the Expression

Step	Order of Operations
3	Simplify the expression $9x^2 + 17$

The expression $9x^2 + 17$ is already simplified.

Conclusion

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Introduction

In our previous article, we explored how to transform the function $f(x) = x^2 + 17$ to $f(-3x)$ using the order of operations. In this article, we will answer some common questions related to transforming functions and the order of operations.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is crucial to ensure that mathematical expressions are evaluated correctly. If the order of operations is not followed, the result of the expression may be incorrect.

Q: How do I apply the order of operations to a mathematical expression?

A: To apply the order of operations to a mathematical expression, follow these steps:

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponential expressions.
3. Evaluate any multiplication and division operations from left to right.
4. Evaluate any addition and subtraction operations from left to right.

Q: What is the difference between a function and a transformation?

A: A function is a mathematical expression that takes one or more input values and produces an output value. A transformation is a change made to a function to create a new function.

Q: How do I transform a function using the order of operations?

A: To transform a function using the order of operations, follow these steps:

1. Replace the variable in the original function with the new variable.
2. Apply the order of operations to simplify the expression.

Q: What are some common types of transformations?

A: Some common types of transformations include:

• Replacing the variable with a multiple of itself
• Replacing the variable with a negative multiple of itself
• Replacing the variable with a fraction of itself
• Replacing the variable with a decimal value

Q: How do I determine the order of operations for a complex expression?

A: To determine the order of operations for a complex expression, follow these steps:

1. Identify any expressions inside parentheses.
2. Identify any exponential expressions.
3. Identify any multiplication and division operations.
4. Identify any addition and subtraction operations.

Q: What are some common mistakes to avoid when applying the order of operations?

A: Some common mistakes to avoid when applying the order of operations include:

• Not following the order of operations
• Not evaluating expressions inside parentheses first
• Not evaluating exponential expressions next
• Not evaluating multiplication and division operations from left to right

Conclusion

In this article, we have answered some common questions related to transforming functions and the order of operations. We have also provided a step-by-step guide on how to apply the order of operations to a mathematical expression. By following the order of operations and avoiding common mistakes, you can ensure that your mathematical expressions are evaluated correctly.

Additional Resources

• Order of Operations Tutorial
• Transforming Functions Tutorial
• Mathematical Expression Evaluator

Practice Problems

• Transform the function $f(x) = 2x^2 + 5$ to $f(-2x)$ using the order of operations.
• Evaluate the expression $3(2x + 1) - 2x^2$ using the order of operations.
• Determine the order of operations for the expression $4x^2 + 2x - 3$.

Answer Key

• Transform the function $f(x) = 2x^2 + 5$ to $f(-2x)$ using the order of operations: $f(-2x) = 4x^2 + 5$
• Evaluate the expression $3(2x + 1) - 2x^2$ using the order of operations: $6x + 3 - 2x^2$
• Determine the order of operations for the expression $4x^2 + 2x - 3$: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.