Question

problem. 1 : find the derivative of the function using the definition of the derivative.
$f(x) = -6x - 9$
$f(x) = -6$
problem. 1.1 : state the domain of the function. (enter your answer using interval notation.)
$\left( \boldsymbol{?}, \boldsymbol{?} \
ight)$

Explanation:

Step1: Identify the function type

The function \( f(x) = -6x - 9 \) is a linear function. Linear functions are of the form \( f(x)=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.

Step2: Determine the domain of a linear function

For a linear function (a polynomial of degree 1), there are no restrictions on the values of \( x \) that we can plug into the function. In other words, \( x \) can be any real number. In interval notation, the set of all real numbers is represented as \( (-\infty, \infty) \).

Answer:

The domain of the function \( f(x)=-6x - 9 \) in interval notation is \( (-\infty, \infty) \). So the first box should be filled with \( -\infty \) and the second box should be filled with \( \infty \).