Calculating Corresponding Values

Oct 13, 2025 by miodeya.com 117 views

Exploring the Function g(x) and Its Corresponding Values

In mathematics, functions play a crucial role in describing the relationship between variables. The function g(x) = 6(3/2)^x is a specific type of function known as an exponential function. In this article, we will explore the function g(x) and determine its corresponding values for the given x-values in the table below. We will also plot each point on the coordinate plane to visualize the behavior of the function.

Understanding the Function g(x)

The function g(x) = 6(3/2)^x is an exponential function, where the base is 3/2 and the exponent is x. The constant 6 is the coefficient of the function. To understand the behavior of the function, let's analyze its components:

The base, 3/2, is a fraction greater than 1, which means the function will increase as x increases.
The exponent, x, determines the rate at which the function increases.
The coefficient, 6, scales the function, making it larger or smaller.

Calculating Corresponding Values

To determine the corresponding values of g(x) for the given x-values, we will substitute each x-value into the function g(x) = 6(3/2)^x and calculate the result.

x	g(x)
-2
-1
0
1
2

Calculating g(-2)

To calculate g(-2), we substitute x = -2 into the function g(x) = 6(3/2)^x:

g(-2) = 6(3/2)^(-2) = 6(1/(3/2)^2) = 6(4/9) = 8/3

Calculating g(-1)

To calculate g(-1), we substitute x = -1 into the function g(x) = 6(3/2)^x:

g(-1) = 6(3/2)^(-1) = 6(2/3) = 4

Calculating g(0)

To calculate g(0), we substitute x = 0 into the function g(x) = 6(3/2)^x:

g(0) = 6(3/2)^0 = 6(1) = 6

Calculating g(1)

To calculate g(1), we substitute x = 1 into the function g(x) = 6(3/2)^x:

g(1) = 6(3/2)^1 = 6(3/2) = 9

Calculating g(2)

To calculate g(2), we substitute x = 2 into the function g(x) = 6(3/2)^x:

g(2) = 6(3/2)^2 = 6(9/4) = 27/2

Plotting the Points

Now that we have calculated the corresponding values of g(x) for the given x-values, we can plot each point on the coordinate plane.

x	g(x)
-2	8/3
-1	4
0	6
1	9
2	27/2

In this article, we explored the function g(x) = 6(3/2)^x and determined its corresponding values for the given x-values in the table below. We also plotted each point on the coordinate plane to visualize the behavior of the function. The function g(x) is an exponential function that increases as x increases, with a base of 3/2 and an exponent of x. The coefficient, 6, scales the function, making it larger or smaller.

In future articles, we can explore other types of functions, such as polynomial and rational functions, and analyze their behavior using various techniques, including graphing and algebraic manipulation. We can also investigate the properties of functions, such as domain and range, and learn how to compose functions to create new functions.

[1] "Functions" by Khan Academy
[2] "Exponential Functions" by Math Open Reference
[3] "Graphing Functions" by Purplemath
Q&A: Exploring the Function g(x) and Its Corresponding Values

In our previous article, we explored the function g(x) = 6(3/2)^x and determined its corresponding values for the given x-values in the table below. We also plotted each point on the coordinate plane to visualize the behavior of the function. In this article, we will answer some frequently asked questions about the function g(x) and its corresponding values.

Q: What is the base of the function g(x)?

A: The base of the function g(x) is 3/2.

Q: What is the exponent of the function g(x)?

A: The exponent of the function g(x) is x.

Q: What is the coefficient of the function g(x)?

A: The coefficient of the function g(x) is 6.

Q: How does the function g(x) behave as x increases?

A: The function g(x) increases as x increases, with a base of 3/2 and an exponent of x.

Q: What is the domain of the function g(x)?

A: The domain of the function g(x) is all real numbers, since the base 3/2 is greater than 1 and the exponent x is a real number.

Q: What is the range of the function g(x)?

A: The range of the function g(x) is all positive real numbers, since the coefficient 6 is positive and the base 3/2 is greater than 1.

Q: How can we calculate the corresponding values of g(x) for a given x-value?

A: To calculate the corresponding values of g(x) for a given x-value, we substitute the x-value into the function g(x) = 6(3/2)^x and calculate the result.

Q: Can we plot the points on the coordinate plane to visualize the behavior of the function g(x)?

A: Yes, we can plot the points on the coordinate plane to visualize the behavior of the function g(x).

Q: What are some real-world applications of the function g(x)?

A: The function g(x) has many real-world applications, such as modeling population growth, chemical reactions, and financial investments.

Q: Can we use the function g(x) to solve problems in other areas of mathematics?

A: Yes, we can use the function g(x) to solve problems in other areas of mathematics, such as algebra, geometry, and trigonometry.

In this article, we answered some frequently asked questions about the function g(x) and its corresponding values. We hope that this article has provided a better understanding of the function g(x) and its behavior.

[1] "Functions" by Khan Academy
[2] "Exponential Functions" by Math Open Reference
[3] "Graphing Functions" by Purplemath