Question

If the function f (x) is the absolute value of 3 more than the value of x. Select all the true statements.

The x-intercept of the function is 3.

The range of the function is (f (x) f(x) E R).

The function is positive in the interval -3 < x < 00.

The function is increasing in the interval -3 < x < [infinity]0.

The function is negative in the interval -[infinity]o < x < -3.

The function is decreasing in the interval -[infinity]o < x < -3

Answer 1

Answer:

• The function is positive in the interval -3 < x < ∞.
• The function is increasing in the interval -3 < x < ∞.
• The function is decreasing in the interval -∞ < x < -3.

Step-by-step explanation:

You want to identify the true statements about the function f(x) = |x+3|.

Graph

A graph of the function is attached. It shows the function is decreasing to the left of x = -3, increasing to the right of that point, and has an x-intercept at x = -3. The function is positive everywhere.

The true descriptions are ...

• The function is positive in the interval -3 < x < ∞.
• The function is increasing in the interval -3 < x < ∞.
• The function is decreasing in the interval -∞ < x < -3.