Can someone please walk me through this problem?
The function f is defined by the following rule,
f(x) = (1/4)^x
Find f(x) for each of these five values
x | f(x)
_ | _______________|
-2 |_______________|
-1 |_______________|
0 |_______________|
1 |_______________|
2 |_______________|
___________________|
You just plug the numbers in for x
First one: (1/4)^-2=16
Second one: (1/4)^-1 = 4
Try the rest on your own. Let me know if you need more help :D
I'll do just 1
Y=f(x)
Y=(1/4)^x
Y=(1/4)^(-2)=1/(1/4)²=1/(1/16)=16
Thank You :)
Sure! Let's go through the problem step by step.
The function is defined as f(x) = (1/4)^x.
To find f(x) for each of the given values of x, we need to substitute each value into the function and calculate the result.
Let's start with x = -2:
f(-2) = (1/4)^(-2)
To calculate x raised to a negative power, we can rewrite it as 1/(x^positive power):
f(-2) = 1 / (1/4)^2
Simplifying the expression inside the parentheses, we get:
f(-2) = 1 / (1/16)
To divide by a fraction, we can multiply by its reciprocal:
f(-2) = 1 * (16/1) = 16
Next, let's calculate for x = -1:
f(-1) = (1/4)^(-1)
Similarly, rewriting it as 1/(1/4)^1, we get:
f(-1) = 1 / (1/4)
To divide by a fraction, remember to multiply by its reciprocal:
f(-1) = 1 * (4/1) = 4
Now, let's calculate for x = 0:
f(0) = (1/4)^0
Any number raised to the power of 0 is always equal to 1:
f(0) = 1
Next, let's calculate for x = 1:
f(1) = (1/4)^1
To raise a fraction to a power, raise the numerator and denominator to that power:
f(1) = 1/4
Finally, let's calculate for x = 2:
f(2) = (1/4)^2
To square a fraction, multiply the numerator and denominator by themselves:
f(2) = (1^2) / (4^2)
Simplifying, we get:
f(2) = 1/16
So, the values of f(x) for the given values of x are as follows:
x | f(x)
-2 | 16
-1 | 4
0 | 1
1 | 1/4
2 | 1/16