Complete The Missing Parts Of The Table For The Following Function.$\[ Y=3^x \\]$\[ \begin{tabular}{c|cccccc} x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & $\frac{1}{9}$ & $\frac{1}{3}$ & 1 & 3 & 9 & 27

Feb 26, 2025 by ADMIN 201 views

Completing the Missing Parts of the Table for the Exponential Function y = 3^x

In mathematics, exponential functions are a fundamental concept that describe the relationship between two variables, where one variable is a constant power of the other. The function y = 3^x is a classic example of an exponential function, where the base is 3 and the exponent is x. In this article, we will explore the concept of completing the missing parts of a table for the function y = 3^x.

Understanding the Function y = 3^x

The function y = 3^x is an exponential function, where the base is 3 and the exponent is x. This means that for every increase in the value of x by 1, the value of y is multiplied by 3. For example, if x = 2, then y = 3^2 = 9. If x = 3, then y = 3^3 = 27.

Completing the Table

The table below shows the values of y for different values of x.

x	y
-2	$\frac{1}{9}$
-1	$\frac{1}{3}$
0	1
1	3
2	9
3	27

To complete the table, we need to find the values of y for x = -3, x = -2, x = -1, x = 2, x = 3, and x = 4.

Finding the Values of y for x = -3, x = -2, x = -1

To find the values of y for x = -3, x = -2, and x = -1, we can use the fact that the function y = 3^x is an exponential function. This means that for every decrease in the value of x by 1, the value of y is divided by 3.

For x = -3, we have y = 3^(-3) = $\frac{1}{3^3}$ = $\frac{1}{27}$ .

For x = -2, we have y = 3^(-2) = $\frac{1}{3^2}$ = $\frac{1}{9}$ .

For x = -1, we have y = 3^(-1) = $\frac{1}{3}$ .

Finding the Values of y for x = 4

To find the value of y for x = 4, we can use the fact that the function y = 3^x is an exponential function. This means that for every increase in the value of x by 1, the value of y is multiplied by 3.

For x = 4, we have y = 3^4 = 3 × 3 × 3 × 3 = 81.

Completing the Table

Now that we have found the values of y for x = -3, x = -2, x = -1, and x = 4, we can complete the table.

x	y
-3	$\frac{1}{27}$
-2	$\frac{1}{9}$
-1	$\frac{1}{3}$
0	1
1	3
2	9
3	27
4	81

In this article, we have explored the concept of completing the missing parts of a table for the function y = 3^x. We have used the fact that the function y = 3^x is an exponential function to find the values of y for x = -3, x = -2, x = -1, and x = 4. We have completed the table and shown that the function y = 3^x is a fundamental concept in mathematics.

The function y = 3^x is a classic example of an exponential function, where the base is 3 and the exponent is x. This function is used in many real-world applications, such as finance, science, and engineering. The concept of completing the missing parts of a table for the function y = 3^x is an important one, as it helps us to understand the behavior of the function and to make predictions about its values.

Find the value of y for x = -5.
Find the value of y for x = 5.
Complete the table for the function y = 2^x.

y = $\frac{1}{243}$
y = 32
x y

-5 $\frac{1}{32}$

-4 $\frac{1}{16}$

-3 $\frac{1}{8}$

-2 $\frac{1}{4}$

-1 $\frac{1}{2}$

0 1

1 2

2 4

3 8

4 16

5 32

x	y
-5	$\frac{1}{32}$
-4	$\frac{1}{16}$
-3	$\frac{1}{8}$
-2	$\frac{1}{4}$
-1	$\frac{1}{2}$
0	1
1	2
2	4
3	8
4	16
5	32

Q&A: Completing the Missing Parts of the Table for the Exponential Function y = 3^x

In our previous article, we explored the concept of completing the missing parts of a table for the function y = 3^x. We used the fact that the function y = 3^x is an exponential function to find the values of y for x = -3, x = -2, x = -1, and x = 4. In this article, we will answer some frequently asked questions about completing the missing parts of the table for the function y = 3^x.

Q: What is the formula for the function y = 3^x?

A: The formula for the function y = 3^x is y = 3^x, where x is the exponent and 3 is the base.

Q: How do I find the values of y for x = -3, x = -2, x = -1, and x = 4?

A: To find the values of y for x = -3, x = -2, x = -1, and x = 4, you can use the fact that the function y = 3^x is an exponential function. This means that for every decrease in the value of x by 1, the value of y is divided by 3, and for every increase in the value of x by 1, the value of y is multiplied by 3.

Q: What is the value of y for x = -5?

A: To find the value of y for x = -5, you can use the fact that the function y = 3^x is an exponential function. This means that for every decrease in the value of x by 1, the value of y is divided by 3. Therefore, y = 3^(-5) = $\frac{1}{3^5}$ = $\frac{1}{243}$ .

Q: What is the value of y for x = 5?

A: To find the value of y for x = 5, you can use the fact that the function y = 3^x is an exponential function. This means that for every increase in the value of x by 1, the value of y is multiplied by 3. Therefore, y = 3^5 = 3 × 3 × 3 × 3 × 3 = 243.

Q: How do I complete the table for the function y = 2^x?

A: To complete the table for the function y = 2^x, you can use the fact that the function y = 2^x is an exponential function. This means that for every increase in the value of x by 1, the value of y is multiplied by 2. You can start with the values of x = -5, x = -4, x = -3, x = -2, x = -1, x = 0, x = 1, x = 2, x = 3, x = 4, and x = 5, and calculate the corresponding values of y.

Q: What is the value of y for x = -4?

A: To find the value of y for x = -4, you can use the fact that the function y = 2^x is an exponential function. This means that for every decrease in the value of x by 1, the value of y is divided by 2. Therefore, y = 2^(-4) = $\frac{1}{2^4}$ = $\frac{1}{16}$ .

Q: What is the value of y for x = 4?

A: To find the value of y for x = 4, you can use the fact that the function y = 2^x is an exponential function. This means that for every increase in the value of x by 1, the value of y is multiplied by 2. Therefore, y = 2^4 = 2 × 2 × 2 × 2 = 16.

In this article, we have answered some frequently asked questions about completing the missing parts of the table for the function y = 3^x. We have used the fact that the function y = 3^x is an exponential function to find the values of y for x = -3, x = -2, x = -1, and x = 4, and to complete the table for the function y = 2^x. We hope that this article has been helpful in understanding the concept of completing the missing parts of the table for the function y = 3^x.

Find the value of y for x = -6.
Find the value of y for x = 6.
Complete the table for the function y = 4^x.

y = $\frac{1}{729}$
y = 4096

x	y
-6	$\frac{1}{4096}$
-5	$\frac{1}{1024}$
-4	$\frac{1}{256}$
-3	$\frac{1}{64}$
-2	$\frac{1}{16}$
-1	$\frac{1}{4}$
0	1
1	4
2	16
3	64
4	256
5	1024
6	4096