Question

What is the range of f(x) = 3^× + 9

Answer 1

The range of the function
`f(x) = 3^x + 9`is all real numbers greater than 9, expressed in interval notation as (9, ∞).

Step-by-step explanation:

The range of the function
`f(x) = 3^x + 9` can be determined by analyzing the behavior of the exponential function. The base, which is 3 in this case, is a positive number greater than 1. Therefore, as x increases, the value of
`3^x` grows larger without bound. This exponential growth occurs for all real values of x. Since every output of
`3^x`is a positive number and adding 9 shifts the graph vertically upward by 9 units, the smallest value f(x) can take on is just above 9, no matter how large or small x is. Therefore, the range of
`f(x) = 3^x + 9` is all real numbers greater than 9, which can be written in interval notation as (9, ∞).

Answer 2

then greater module(abs value) of negative x , than smaller will be 3^x, 3^x will go to the zero,
so range is (9,∞)