Evaluating the Function for Given Values of x

Oct 13, 2025 by thesweetdesigns.com 102 views

Evaluating the Function f(x) = (1/2)^x for Given Values of x

In this article, we will evaluate the function f(x) = (1/2)^x for the given values of x and complete the table below. The function f(x) is an exponential function with base 1/2, and we will use this function to calculate the values of y for the given values of x.

The Function f(x) = (1/2)^x

The function f(x) = (1/2)^x is an exponential function with base 1/2. This function can be written in the form f(x) = a^x, where a is the base and x is the exponent. In this case, the base is 1/2.

Evaluating the Function for Given Values of x

To evaluate the function f(x) = (1/2)^x for the given values of x, we will substitute the values of x into the function and calculate the corresponding values of y.

Evaluating f(-3)

To evaluate f(-3), we will substitute x = -3 into the function f(x) = (1/2)^x.

f(-3) = (1/2)^(-3) = 1 / (1/2)^3 = 1 / (1/8) = 8

Therefore, f(-3) = 8.

Evaluating f(-2)

To evaluate f(-2), we will substitute x = -2 into the function f(x) = (1/2)^x.

f(-2) = (1/2)^(-2) = 1 / (1/2)^2 = 1 / (1/4) = 4

Therefore, f(-2) = 4.

Evaluating f(-1)

To evaluate f(-1), we will substitute x = -1 into the function f(x) = (1/2)^x.

f(-1) = (1/2)^(-1) = 1 / (1/2) = 2

Therefore, f(-1) = 2.

Completing the Table

Based on the evaluations above, we can complete the table below.

x	y = f(x)
-3	8
-2	4
-1	2

In this article, we evaluated the function f(x) = (1/2)^x for the given values of x and completed the table below. We used the function to calculate the values of y for the given values of x and found that f(-3) = 8, f(-2) = 4, and f(-1) = 2.

The function f(x) = (1/2)^x is an exponential function with base 1/2. This function can be used to model real-world phenomena, such as population growth or decay. The function can also be used to calculate the values of y for given values of x.

Evaluate the function f(x) = (1/2)^x for x = -4, -5, and -6.
Complete the table below for the function f(x) = (1/2)^x.

x	y = f(x)
-3	8
-2	4
-1	2
0	1
1	1/2
2	1/4
3	1/8

f(-4) = 16, f(-5) = 32, f(-6) = 64.
The completed table is shown below.

x	y = f(x)
-3	8
-2	4
-1	2
0	1
1	1/2
2	1/4
3	1/8
4	1/16
5	1/32
6	1/64

In our previous article, we evaluated the function f(x) = (1/2)^x for the given values of x and completed the table below. In this article, we will answer some frequently asked questions about the function f(x) = (1/2)^x.

Q: What is the base of the function f(x) = (1/2)^x?

A: The base of the function f(x) = (1/2)^x is 1/2.

Q: What is the exponent of the function f(x) = (1/2)^x?

A: The exponent of the function f(x) = (1/2)^x is x.

Q: How do you evaluate the function f(x) = (1/2)^x for a given value of x?

A: To evaluate the function f(x) = (1/2)^x for a given value of x, you can use the formula f(x) = (1/2)^x. For example, to evaluate f(-3), you would substitute x = -3 into the formula and calculate the result.

Q: What is the value of f(-3)?

A: The value of f(-3) is 8.

Q: What is the value of f(-2)?

A: The value of f(-2) is 4.

Q: What is the value of f(-1)?

A: The value of f(-1) is 2.

Q: Can you complete the table below for the function f(x) = (1/2)^x?

x	y = f(x)
-3	8
-2	4
-1	2
0	1
1	1/2
2	1/4
3	1/8
4	1/16
5	1/32
6	1/64

A: Yes, the completed table is shown below.

x	y = f(x)
-3	8
-2	4
-1	2
0	1
1	1/2
2	1/4
3	1/8
4	1/16
5	1/32
6	1/64

Q: What is the pattern of the values in the table?

A: The pattern of the values in the table is that each value is half of the previous value.

Q: Can you evaluate the function f(x) = (1/2)^x for x = -4, -5, and -6?

A: Yes, the values of f(-4), f(-5), and f(-6) are 16, 32, and 64, respectively.

In this article, we answered some frequently asked questions about the function f(x) = (1/2)^x. We also completed the table below for the function and evaluated the function for x = -4, -5, and -6.

Evaluate the function f(x) = (1/2)^x for x = -7, -8, and -9.
Complete the table below for the function f(x) = (1/2)^x.

x	y = f(x)
-7	128
-8	256
-9	512
0	1
1	1/2
2	1/4
3	1/8
4	1/16
5	1/32
6	1/64

f(-7) = 512, f(-8) = 1024, f(-9) = 2048.
The completed table is shown below.

x	y = f(x)
-7	128
-8	256
-9	512
0	1
1	1/2
2	1/4
3	1/8
4	1/16
5	1/32
6	1/64
7	1/128
8	1/256
9	1/512