Question

What is the range of f(x) = 3* + 9?

{yly<9}
{yly > 9}
{yly > 3}
{yly <3}

Answer 1

{y l y > 9}

Explanation:

Given function:

`f(x)=3^x+9`

The given function is an exponential function.

The parent function is the basic equation before the function has undergone any transformation(s). Therefore, the parent function of the given function is:

• 
  `f(x) = 3^x`

The range of the parent function is restricted to positive real numbers as it never takes a negative value. Furthermore, it never reaches zero (although it approaches y = 0 as x → -∞). Therefore, the range of the parent function is y .

As the given function has been translated up 9 units (by the addition of "+ 9"), the range of the given function is translated 9 units up. So as x approaches negative infinity, y approaches (but never reaches) 9. Therefore, the range of the given function is:

• y > 9