Question

What are the domain and range of the function f(x) = 3^x + 5

Answer 1

• the domain of the function - all real numbers;
• the range of the function - all real numbers
  `y>5.`

Explanation:

Consider the parent function
`y=3^x.` The base of this exponential function is
`3>0,` then the function is increasing and

• the domain of the function - all real numbers;
• the range of the function - all positive real numbers
  `y>0.`

The graph of the function
`f(x)=3^x+5` is translated 5 units up graph of the parent function (see attached diagram).

Thus,

• the domain of the function - all real numbers;
• the range of the function - all real numbers
  `y>5.`