Substituting the Input Value

Oct 13, 2025 by talynt.org 149 views

Understanding the Function

The given function is $g(x) = 3x - 3$ . This is a linear function, where the output value is determined by multiplying the input value by a constant factor (in this case, 3) and then subtracting a constant value (in this case, 3).

Substituting the Input Value

To find the value of $g(7)$ , we need to substitute $x = 7$ into the function. This means we replace every instance of $x$ with 7.

Evaluating the Function

Now that we have substituted the input value, we can evaluate the function by following the order of operations (PEMDAS):

Multiply 7 by 3: $7 \times 3 = 21$
Subtract 3 from the result: $21 - 3 = 18$

Selecting the Correct Answer

Based on our evaluation, the value of $g(7)$ is 18. Therefore, the correct answer is:

C. 18

Why the Other Options Are Incorrect

Let's take a look at the other options to see why they are incorrect:

A. 21: This is the result of multiplying 7 by 3, but we need to subtract 3 to get the final answer.
B. 3.33: This is not a possible result of the function $g(x) = 3x - 3$ , as the output will always be an integer.
D. 24: This is not a possible result of the function $g(x) = 3x - 3$ , as the output will always be an integer.

Conclusion

In conclusion, the value of $g(7)$ is 18. This is a simple example of how to evaluate a linear function, and it demonstrates the importance of following the order of operations and substituting the input value correctly.

Real-World Applications

This type of problem may seem trivial, but it has real-world applications in many fields, such as:

Science: In physics, the value of a function may represent the position or velocity of an object.
Engineering: In engineering, the value of a function may represent the output of a system or the result of a calculation.
Finance: In finance, the value of a function may represent the value of an investment or the result of a financial calculation.

Tips and Tricks

Here are some tips and tricks to help you evaluate functions like this:

Read the problem carefully: Make sure you understand what the function is and what the input value is.
Substitute the input value: Replace every instance of the input variable with the given value.
Follow the order of operations: Evaluate the function by following the order of operations (PEMDAS).
Check your units: Make sure the units of the output value are correct.

Practice Problems

Here are some practice problems to help you practice evaluating functions:

Find the value of $f(5)$ for the function $f(x) = 2x + 1$
Find the value of $g(3)$ for the function $g(x) = x^2 - 2x + 1$
Find the value of $h(2)$ for the function $h(x) = \frac{x}{2} + 1$

Conclusion

In conclusion, evaluating functions is an important skill that has many real-world applications. By following the order of operations and substituting the input value correctly, you can find the value of a function with ease. Remember to read the problem carefully, check your units, and practice regularly to become proficient in evaluating functions.

Q: What is a function?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). It is a way of describing a relationship between variables, where each input corresponds to exactly one output.

Q: What is the difference between a function and an equation?

A: An equation is a statement that two expressions are equal, while a function is a relation between a set of inputs and a set of possible outputs. In other words, an equation is a statement that two values are equal, while a function is a way of describing a relationship between variables.

Q: How do I evaluate a function?

A: To evaluate a function, you need to substitute the input value into the function and follow the order of operations (PEMDAS). This means that you need to:

Read the problem carefully and understand what the function is and what the input value is.
Substitute the input value into the function.
Follow the order of operations (PEMDAS) to evaluate the function.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:

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

Q: How do I know which operations to perform first?

A: To determine which operations to perform first, you need to follow the order of operations (PEMDAS). This means that you need to:

Evaluate any expressions inside parentheses first.
Evaluate any exponential expressions next.
Evaluate any multiplication and division operations from left to right.
Finally, evaluate any addition and subtraction operations from left to right.

Q: What if I have multiple operations with the same precedence?

A: If you have multiple operations with the same precedence, you need to perform them from left to right. This means that you need to evaluate the operations in the order that they appear from left to right.

Q: Can I use a calculator to evaluate a function?

A: Yes, you can use a calculator to evaluate a function. However, it's always a good idea to double-check your work by hand to make sure that you understand the function and the order of operations.

Q: How do I know if a function is linear or non-linear?

A: A function is linear if it can be written in the form f(x) = mx + b, where m and b are constants. If a function cannot be written in this form, it is non-linear.

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

A: A linear function is a function that can be written in the form f(x) = mx + b, where m and b are constants. A quadratic function is a function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Q: How do I graph a function?

A: To graph a function, you need to plot points on a coordinate plane and connect them with a smooth curve. You can use a graphing calculator or software to help you graph the function.

Q: What is the domain of a function?

A: The domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of all possible x-values for which the function is defined.

Q: What is the range of a function?

A: The range of a function is the set of all possible output values for which the function is defined. In other words, it is the set of all possible y-values for which the function is defined.

Q: How do I find the domain and range of a function?

A: To find the domain and range of a function, you need to analyze the function and determine the set of all possible input values and output values for which the function is defined.

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

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A relation is a set of ordered pairs that satisfy a certain condition.

Q: How do I determine if a relation is a function?

A: To determine if a relation is a function, you need to check if each input value corresponds to exactly one output value. If each input value corresponds to exactly one output value, then the relation is a function.

Q: What is the difference between a function and an equation?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). An equation is a statement that two expressions are equal.

Q: How do I evaluate a function with multiple variables?

A: To evaluate a function with multiple variables, you need to substitute the input values into the function and follow the order of operations (PEMDAS).

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

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A formula is a mathematical expression that describes a relationship between variables.

Q: How do I determine if a function is increasing or decreasing?

A: To determine if a function is increasing or decreasing, you need to analyze the function and determine if the output value increases or decreases as the input value increases.

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

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A graph is a visual representation of a function.

Q: How do I graph a function with multiple variables?

A: To graph a function with multiple variables, you need to plot points on a coordinate plane and connect them with a smooth curve. You can use a graphing calculator or software to help you graph the function.

Q: What is the difference between a function and a relation with multiple variables?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A relation with multiple variables is a set of ordered pairs that satisfy a certain condition.

Q: How do I determine if a relation with multiple variables is a function?

A: To determine if a relation with multiple variables is a function, you need to check if each input value corresponds to exactly one output value. If each input value corresponds to exactly one output value, then the relation is a function.

Q: What is the difference between a function and an equation with multiple variables?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). An equation with multiple variables is a statement that two expressions are equal.

Q: How do I evaluate a function with multiple variables and multiple operations?

A: To evaluate a function with multiple variables and multiple operations, you need to substitute the input values into the function and follow the order of operations (PEMDAS).

Q: What is the difference between a function and a formula with multiple variables?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A formula with multiple variables is a mathematical expression that describes a relationship between variables.

Q: How do I determine if a function is linear or non-linear with multiple variables?

A: To determine if a function is linear or non-linear with multiple variables, you need to analyze the function and determine if it can be written in the form f(x) = mx + b, where m and b are constants.

Q: What is the difference between a function and a graph with multiple variables?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A graph with multiple variables is a visual representation of a function.

Q: How do I graph a function with multiple variables and multiple operations?

A: To graph a function with multiple variables and multiple operations, you need to plot points on a coordinate plane and connect them with a smooth curve. You can use a graphing calculator or software to help you graph the function.

Q: What is the difference between a function and a relation with multiple variables and multiple operations?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A relation with multiple variables and multiple operations is a set of ordered pairs that satisfy a certain condition.

Q: How do I determine if a relation with multiple variables and multiple operations is a function?

A: To determine if a relation with multiple variables and multiple operations is a function, you need to check if each input value corresponds to exactly one output value. If each input value corresponds to exactly one output value, then the relation is a function.