Complete The Table Of Inputs And Outputs For The Given Function. Type The Correct Answer In Each Box. Use Numerals Instead Of Words. If Necessary, Use / For The Fraction Bar.Given Function: $g(x) = 3 - 8x$\[ \begin{array}{|c|c|} \hline x

Introduction

In mathematics, functions are used to describe the relationship between two variables. A function is a rule that assigns to each input a unique output. In this article, we will complete the table of inputs and outputs for the given function $g(x) = 3 - 8x$. We will use numerals instead of words and fractions with a bar to represent the output values.

The Given Function

The given function is $g(x) = 3 - 8x$. This function takes an input value $x$ and produces an output value $g(x)$.

Table of Inputs and Outputs

$x$	$g(x)$
0
1
2
3
4

Calculating the Output Values

To complete the table, we need to calculate the output values for each input value. We can do this by substituting the input value into the function and simplifying the expression.

Calculating $g(0)$

To calculate $g(0)$, we substitute $x = 0$ into the function:

$$g(0) = 3 - 8(0)$$

Simplifying the expression, we get:

$$g(0) = 3 - 0$$

$$g(0) = 3$$

Calculating $g(1)$

To calculate $g(1)$, we substitute $x = 1$ into the function:

$$g(1) = 3 - 8(1)$$

Simplifying the expression, we get:

$$g(1) = 3 - 8$$

$$g(1) = -5$$

Calculating $g(2)$

To calculate $g(2)$, we substitute $x = 2$ into the function:

$$g(2) = 3 - 8(2)$$

Simplifying the expression, we get:

$$g(2) = 3 - 16$$

$$g(2) = -13$$

Calculating $g(3)$

To calculate $g(3)$, we substitute $x = 3$ into the function:

$$g(3) = 3 - 8(3)$$

Simplifying the expression, we get:

$$g(3) = 3 - 24$$

$$g(3) = -21$$

Calculating $g(4)$

To calculate $g(4)$, we substitute $x = 4$ into the function:

$$g(4) = 3 - 8(4)$$

Simplifying the expression, we get:

$$g(4) = 3 - 32$$

$$g(4) = -29$$

Completed Table

$x$	$g(x)$
0	3
1	-5
2	-13
3	-21
4	-29

Conclusion

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Introduction

In our previous article, we completed the table of inputs and outputs for the given function $g(x) = 3 - 8x$. In this article, we will answer some frequently asked questions related to the topic.

Q: What is the purpose of completing the table of inputs and outputs for a function?

A: The purpose of completing the table of inputs and outputs for a function is to visualize the relationship between the input values and the output values. This helps us to understand the behavior of the function and make predictions about its output for different input values.

Q: How do I calculate the output values for a function?

A: To calculate the output values for a function, you need to substitute the input value into the function and simplify the expression. For example, if the function is $g(x) = 3 - 8x$ and the input value is $x = 2$, you would substitute $x = 2$ into the function and simplify the expression to get the output value.

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

A: A function is a rule that assigns to each input a unique output, while an equation is a statement that two expressions are equal. For example, the equation $x + 2 = 5$ is not a function because it does not assign a unique output to each input. However, the function $g(x) = 3 - 8x$ is a function because it assigns a unique output to each input.

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

A: To determine if a function is linear or non-linear, you need to examine its graph or table of inputs and outputs. If the graph or table shows a straight line, the function is linear. If the graph or table shows a curve, the function is non-linear.

Q: What is the significance of the slope of a linear function?

A: The slope of a linear function represents the rate of change of the output value with respect to the input value. For example, if the function is $g(x) = 3 - 8x$ and the slope is -8, it means that for every unit increase in the input value, the output value decreases by 8 units.

Q: How do I use the table of inputs and outputs to make predictions about the function?

A: To make predictions about the function, you can use the table of inputs and outputs to identify patterns and trends. For example, if the table shows that the output value increases by 5 units for every unit increase in the input value, you can predict that the output value will continue to increase by 5 units for every unit increase in the input value.

Q: What are some common applications of functions in real-life situations?

A: Functions are used in a wide range of real-life situations, including:

• Modeling population growth and decline
• Describing the motion of objects
• Analyzing the behavior of electrical circuits
• Predicting the outcome of economic systems
• Optimizing the performance of machines and systems

Conclusion

In this article, we answered some frequently asked questions related to completing the table of inputs and outputs for a function. We hope that this article has provided you with a better understanding of the topic and has helped you to develop your skills in working with functions.