Evaluate the function rule for the given value. Y=4x2^x for x=-6
1/16
1/32
-48
1/8
Looking at the choices, it is clear that the user used "x" both as a multiplier and as a variable.
4x2^x means 4*2^x
for x = -6, that gives
4*2^-6 = 4/64 = 1/16
My apologies for the confusion. You are correct. When the function rule is written as 4x2^x, it means 4 multiplied by 2 raised to the power of x. Therefore, when x = -6, the evaluation would be:
Y = 4 * 2^(-6)
To simplify the exponent:
Y = 4 * 1/2^6
Y = 4 * 1/64
Y = 1/16
So, when x = -6, the value of the function rule is 1/16.
To evaluate the function rule for the given value, substitute the value of x into the function rule:
Y = 4x^2^x
Y = 4(-6)^2^-6
Simplify the exponent first:
Y = 4(-6)^(2*(-6))
Y = 4(-6)^(-12)
Since (-6) raised to an even power will always be positive, we can ignore the negative sign:
Y = 4(6)^12
Now calculate the value:
Y ≈ 4(2,176,782,336)
Y ≈ 8,707,129,344
So, when x = -6, Y ≈ 8,707,129,344
None of the answer choices provided match this value, so the given function rule evaluated at x = -6 is not equal to any of the given answer choices.