What is the range of the function

f(x)=3-2*51^x? Give your answer as an interval.

as x is hugely negative, 2*51^x ---->

so f(x) ----> 3 - 0 or 3
as x becomes hugely positive -2*51^x --->- ∞

do the range is y < 3

I will let you use whatever notation you have learned

forgot the zero in the first line , should read:

as x is hugely negative, 2*51^x ----> 0

To find the range of a function, we need to determine all possible values that the function can output. In other words, we need to find the set of all possible y-values in the function.

To find the range of the function f(x) = 3 - 2*51^x, we can start by considering the behavior of the exponential term, 51^x.

Since 51 raised to any power will always yield a positive number, the term 51^x will always be positive. This means that the term -2*51^x will always be negative.

Next, we add the constant term 3 to the negative term -2*51^x. Adding a positive constant to a negative term will shift the entire range upwards towards positive values. Therefore, the range of f(x) = 3 - 2*51^x will be all real numbers less than or equal to 3.

Expressing this as an interval, we can represent the range as (-∞, 3], where the parentheses indicate that negative infinity is not included, and the bracket indicates that 3 is included.