For the given function, compute the missing values in the following table.
f(x) = 8x
i got the negatives wrong, but I know how to solve for it. Is there a reason it is wrong?
-3: -1/512
-2: -1/64
-1: -1/8
(^These were wrong, but I don't know how to solve it)
0: 1
1: 8
2: 64
3: 512
(^These are correct.)
How should I approach the problem of finding negative exponential values?
Thank you
f ( x ) = 8 ^ x
x = 0
8 ^ 0 = 1
x = 1
8 ^ 1 = 8
x = 2
8 ^ 2 = 64
x = 3
8 ^ 3 = 512
To compute the missing values for negative exponents in the table for the given function f(x) = 8x, you need to evaluate the function for negative values of x.
To solve for negative values in exponents, you can use the property that says any nonzero number raised to a negative exponent is equal to 1 divided by the number raised to the positive exponent. In other words, for any nonzero number a and any negative integer n, a^(-n) = 1 / (a^n).
Applying this property to the function f(x) = 8x, you can compute the missing values as follows:
-3: 8^(-3) = 1 / (8^3) = 1 / 512 (which was incorrect)
-2: 8^(-2) = 1 / (8^2) = 1 / 64 (which was incorrect)
-1: 8^(-1) = 1 / (8^1) = 1 / 8 (which was incorrect)
So, the correct values for the negative exponents are:
-3: 1 / (8^3) = 1 / 512
-2: 1 / (8^2) = 1 / 64
-1: 1 / (8^1) = 1 / 8
I hope this clarifies the correct approach in finding the missing negative exponential values in the table.
To find the missing values for negative exponential values in the given function f(x) = 8x, you need to understand the concept of negative exponents.
In general, the formula for a number raised to a negative exponent is as follows: a^(-n) = 1/(a^n), where "a" is the base and "n" is the exponent.
Using this formula, we can calculate the missing values for negative x-values in the table.
For example, let's take the first missing value, f(-3):
f(-3) = 8^(-3)
Using the formula, we can rewrite it as:
f(-3) = 1/(8^3) = 1/512
So, the correct value for f(-3) is 1/512.
Similarly, you can calculate the missing values for the rest of the negative x-values using the same approach:
f(-2) = 1/(8^2) = 1/64
f(-1) = 1/(8^1) = 1/8
By applying the formula a^(-n) = 1/(a^n), you can correctly calculate the missing values for negative x-values and complete the table.
Remember to be careful with negative exponents and make sure you correctly convert them using the formula mentioned above.
Hope this explanation clarifies the approach to find the missing negative exponential values in the table. If you have any further questions, feel free to ask!
x = - 1
8 ^ - 1 = 1 / 8
x = - 2
8 ^ - 2 = 1 / 8 ^ 2 = 1 / 64
x = - 3
8 ^ - 3 = 1 / 8 ^ 3 = 1 / 512