The graphs of f (x) and g (x) are shown below.

On a coordinate plane, a straight line with a positive slope represents f (x) = x minus 3. The line goes through (0, negative 3) and (3, 0). On a coordinate plane, a straight line with a negative slope represents g (x) = negative 0.5 x. The line goes through (negative 4, 2), (0, 0), and (4, negative 2)

For what interval is the value of (f - g) (x) negative?

(negative infinity, negative 1)

(negative infinity, 2)

(0, 3)

(2, infinity)

Question

Mathematics

Finnegan Glenn

11 February, 03:04

The graphs of f (x) and g (x) are shown below.

On a coordinate plane, a straight line with a positive slope represents f (x) = x minus 3. The line goes through (0, negative 3) and (3, 0). On a coordinate plane, a straight line with a negative slope represents g (x) = negative 0.5 x. The line goes through (negative 4, 2), (0, 0), and (4, negative 2)

For what interval is the value of (f - g) (x) negative?

(negative infinity, negative 1)

(negative infinity, 2)

(0, 3)

(2, infinity)

+5

Answers (1)

Know the Answer?

Autumn Gray · Answer 1

(negative infinity, 2)

Step-by-step explanation:

The two functions are given by f (x) = x - 3 and g (x) = - 0.5x

So, (f - g) (x) = x - 3 - ( - 0.5x) = 1.5x - 3

Then, for (f - g) (x) to be negative (1.5x - 3) < 0

⇒ 1.5x < 3

⇒ x < 2

Therefore, the interval will be (negative infinity, 2) for which the function (f - g) (x) will be negative. (Answer)