Find the domain and range of the function y = 2 ^ 3x-6 + 4

Let’s find the domain of the function:

In our function, the variable x is an exponent. In this case, x can be anything, that is, be both negative and positive, and take the value 0. Therefore, x can take values ​​from minus infinity to plus infinity.

Find the range of values ​​of the function:

The minimum value that the first term of the expression can take tends to 0 (the case when x tends to minus infinity).

Substitute 0 for the first term:

y = 0 – 6 + 4;

y = -2.

A value of -2 is not reached because a value of 0 is not reached on the first term. With an increase in the value of x, the right side of the function will always increase, therefore, y> -2.

Answer: y> -2; x can take values ​​from minus infinity to plus infinity.