Evaluate The Function F ( X ) = 7 X + 1 F(x) = 7x + 1 F ( X ) = 7 X + 1 At The Given Values Of The Independent Variable And Simplify.a. F ( 3 F(3 F ( 3 ] B. F ( X + 4 F(x+4 F ( X + 4 ] C. F ( − X F(-x F ( − X ] A. F ( 3 ) = □ F(3) = \square F ( 3 ) = □ (Simplify Your Answer.)

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Introduction

In mathematics, functions are used to describe the relationship between variables. A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). In this article, we will evaluate the function $f(x) = 7x + 1$ at given values of the independent variable and simplify the results.

Evaluating $f(3)$

To evaluate $f(3)$, we need to substitute $x = 3$ into the function $f(x) = 7x + 1$. This means we will replace every instance of $x$ with $3$ and then simplify the expression.

$f(3) = 7(3) + 1$

Using the distributive property, we can multiply $7$ by $3$ to get $21$.

$f(3) = 21 + 1$

Now, we can add $21$ and $1$ to get the final result.

$f(3) = 22$

Evaluating $f(x+4)$

To evaluate $f(x+4)$, we need to substitute $x+4$ into the function $f(x) = 7x + 1$. This means we will replace every instance of $x$ with $x+4$ and then simplify the expression.

$f(x+4) = 7(x+4) + 1$

Using the distributive property, we can multiply $7$ by $x+4$ to get $7x+28$.

$f(x+4) = 7x+28 + 1$

Now, we can add $7x+28$ and $1$ to get the final result.

$f(x+4) = 7x+29$

Evaluating $f(-x)$

To evaluate $f(-x)$, we need to substitute $-x$ into the function $f(x) = 7x + 1$. This means we will replace every instance of $x$ with $-x$ and then simplify the expression.

$f(-x) = 7(-x) + 1$

Using the distributive property, we can multiply $7$ by $-x$ to get $-7x$.

$f(-x) = -7x + 1$

Conclusion

In this article, we evaluated the function $f(x) = 7x + 1$ at given values of the independent variable and simplified the results. We found that $f(3) = 22$, $f(x+4) = 7x+29$, and $f(-x) = -7x + 1$. These results demonstrate the importance of evaluating functions at specific values of the independent variable and simplifying the resulting expressions.

Final Thoughts

Evaluating functions at specific values of the independent variable is a crucial step in understanding the behavior of functions. By simplifying the resulting expressions, we can gain valuable insights into the properties of functions and make informed decisions in a variety of mathematical and real-world applications.

References

• [1] "Functions" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra-functions
• [2] "Evaluating Functions" by Math Open Reference. Retrieved from https://www.mathopenref.com/evaluatingfunctions.html

Related Topics

• [1] "Linear Functions" by Math Is Fun. Retrieved from https://www.mathisfun.com/algebra/linear-functions.html
• [2] "Function Notation" by Purplemath. Retrieved from https://www.purplemath.com/modules/functn.htm

Keywords

• Function
• Independent variable
• Evaluating functions
• Simplifying expressions
• Linear functions
• Function notation
  

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Introduction

In our previous article, we evaluated the function $f(x) = 7x + 1$ at given values of the independent variable and simplified the results. In this article, we will answer some frequently asked questions (FAQs) related to evaluating functions and simplifying expressions.

Q&A

Q: What is the difference between evaluating a function and simplifying an expression?

A: Evaluating a function involves substituting a specific value of the independent variable into the function and simplifying the resulting expression. Simplifying an expression, on the other hand, involves rewriting the expression in a simpler form, often by combining like terms or using algebraic properties.

Q: How do I evaluate a function at a specific value of the independent variable?

A: To evaluate a function at a specific value of the independent variable, you need to substitute the value into the function and simplify the resulting expression. For example, to evaluate $f(x) = 7x + 1$ at $x = 3$, you would substitute $3$ into the function and simplify to get $f(3) = 22$.

Q: What is the distributive property, and how is it used in evaluating functions?

A: The distributive property is a mathematical property that states that for any numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This property is used in evaluating functions by allowing us to multiply a coefficient by a binomial or polynomial expression.

Q: How do I simplify an expression involving like terms?

A: To simplify an expression involving like terms, you need to combine the like terms by adding or subtracting their coefficients. For example, to simplify the expression $2x + 3x$, you would combine the like terms to get $5x$.

Q: What is the difference between a linear function and a nonlinear function?

A: A linear function is a function that can be written in the form $f(x) = ax + b$, where $a$ and $b$ are constants. A nonlinear function, on the other hand, is a function that cannot be written in this form. Examples of nonlinear functions include quadratic functions, cubic functions, and exponential functions.

Q: How do I determine whether a function is linear or nonlinear?

A: To determine whether a function is linear or nonlinear, you need to examine its graph or equation. If the graph is a straight line, the function is linear. If the graph is a curve, the function is nonlinear.

Conclusion

In this article, we answered some frequently asked questions related to evaluating functions and simplifying expressions. We hope that this Q&A article has provided you with a better understanding of these important mathematical concepts.

Final Thoughts

Evaluating functions and simplifying expressions are essential skills in mathematics and are used in a variety of real-world applications. By mastering these skills, you will be able to solve problems and make informed decisions in a variety of mathematical and real-world contexts.

References

• [1] "Functions" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra-functions
• [2] "Evaluating Functions" by Math Open Reference. Retrieved from https://www.mathopenref.com/evaluatingfunctions.html

Related Topics

• [1] "Linear Functions" by Math Is Fun. Retrieved from https://www.mathisfun.com/algebra/linear-functions.html
• [2] "Function Notation" by Purplemath. Retrieved from https://www.purplemath.com/modules/functn.htm

Keywords

• Function
• Independent variable
• Evaluating functions
• Simplifying expressions
• Linear functions
• Nonlinear functions
• Distributive property
• Like terms