Question

What is the domain of the function f(x) = x2 + 3x + 5

Answer 1

The domain of the function is defined as x-values that result in valid y-values. In this case, the domain -∞ < x < ∞ satisfies the function because all real numbers in x result in a real y-value.

Answer 2

The domain is all real numbers

Explanation:

we have

`f(x) = x^(2)+ 3x + 5`

This is the equation of a vertical parabola open upward

The vertex is a minimum

Using a graphing tool

see the attached figure

The vertex is the point
`(-1.5,2.75)`

The range is the interval-------> [2.75.∞)

`y\geq2.75` -------> All real numbers greater than or equal to
`2.75`

The domain is the interval -------> (-∞,∞) -----> All real numbers