Question

Determine the minimum value of the function f(x)=4^x-8. How would you know?
a) 0
b) -8
c) 4
d) no minimum value exists

Answer 1

Which function is f(x)?

\[\Large f(x) = 4^{x} - 8\]

\[\Large f(x) = 4^{x - 8}\]

Answer 2

f(x) = 4x - 8
y=4x-8 replace f(x) with y
x=4y-8 switch values and solve for y.
4y=x+8
y=x/4+2

Answer 3

f(x) is the first one

Answer 4

focus on just 4^x

what happens to the overall expression of 4^x when x is a large negative number (like x = -100) ?

Answer 5

when x is large, the expression is very small

Answer 6

a large negative, yes

essentially 4^x will approach 0 when x approaches negative infinity

so (4^x) - 8 will approach -8 when x approaches negative infinity

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BUT -8 is NOT the minimum because the function output actually never ever gets to -8. It only gets closer and closer. It turns out that there is no minimum because the curve simply approaches this value in the form of a horizontal asymptote.