What is the domain and range fro the expentiral function f(x)=-2x4^x-1+3?

Question

Domain:all real numbers
Range:all real numbers less than 3

Domain:all real numbers
Range:all real numbers greater than 3

Domain: all real numbers greater than-2
Range: all real numbers less than 3

Domain: all real numbers
Range: all real numbers

If the parent function is f(x) = (0.5)^x, which transformations are required for the graph of f(x) = (0.5)^x-3 - 2?


Translate 3 units right and 2 units up

Translate 3 units right and 2 units down

Translate 3 units left and 2 units up

Translate 3 units left and 2 units down

How do I figure something like this out... I'm lost once again

Answer 1

Assuming you meant

f(x)=-2x*4^(x-1)+3
the domain of all polynomials (-2x) is (-∞,∞)
the domain of all exponentials is (-∞,∞)
so, the domain of f(x) is likewise (-∞,∞)

now work with the ranges in like wise.

x -> (x-h) translates right by h
y -> (y-k) translates up by k

y = 0.5^(x-3) - 2 is also
y-(-2) = 0.5^(x-3)

so what do you think?

Answer 2

Thanks Mr.Steve!