Complete the table of values for the function y = 4(1^x/2)^x:
x -3 -2 -1 0 1 2 3
y ___ ____ _____ ____ ____ ____ __
clarify if you meant it the way you typed it, or if you meant 4(1^(x/2) )^x
remember that 1^anything = 1
so the way you typed it, it would simply become
y = 4(1/2)^x
if you meant: y = 4(1^(x/2) )^x , then we have
y = 4(1)^x or simply
y = 4
To complete the table of values for the given function y = 4(1^x/2)^x, you need to substitute each value of x into the function and solve for y.
Let's go through the values one by one:
For x = -3:
y = 4(1^(-3/2))^(-3)
The exponent -3/2 means the reciprocal of the square root of 1, which is still 1 since the square root of 1 is 1.
y = 4(1^1)^(-3)
Since any number raised to the power of 1 is still the same number, we have:
y = 4(1)^(-3)
Since any number raised to the power of 0 is 1, we can write this as:
y = 4/1
y = 4
For x = -2:
y = 4(1^(-2/2))^(-2)
Again, the exponent -2/2 means the reciprocal of the square root of 1, which is still 1.
y = 4(1^1)^(-2)
y = 4(1)^(-2)
y = 4(1/1)
y = 4
For x = -1:
y = 4(1^(-1/2))^(-1)
Once again, the exponent -1/2 means the reciprocal of the square root of 1, which is still 1.
y = 4(1^1)^(-1)
y = 4(1)^(-1)
y = 4(1)
y = 4
For x = 0:
y = 4(1^(0/2))^0
The exponent 0/2 is 0, and any number raised to the power of 0 is 1.
y = 4(1^0)
y = 4(1)
y = 4
For x = 1:
y = 4(1^(1/2))^1
The exponent 1/2 represents the square root of 1, which is 1.
y = 4(1^1)
y = 4(1)
y = 4
For x = 2:
y = 4(1^(2/2))^2
The exponent 2/2 is 1, so any number raised to the power of 1 is still the same number.
y = 4(1^1)^2
y = 4(1)^2
y = 4(1)
y = 4
For x = 3:
y = 4(1^(3/2))^3
The exponent 3/2 represents the square root of 1, which is 1.
y = 4(1^1)^3
y = 4(1)^3
y = 4(1)
y = 4
Therefore, the completed table of values is:
x -3 -2 -1 0 1 2 3
y 4 4 4 4 4 4 4