Question

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)

Answer 1

Answer:

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Answer 2

Answer:

(negative infinity,2)

Step-by-step explanation:

We are given that a straight line with positive slope

$f(x)=x-3$

The line passing through (0,-3) and (3,0).

$g(x)=-0.5 x$

The line goes through (-4,2),(0,0) and (4,-2).

We have to find in which interval the value  of (f-g)(x) is negative.

$(f-g)(x)=x-3+0.5x=1.5x-3$

When x is negative then (f-g)(x) is negative when x is positive except at x=2 then (f-g)(x) is positive.When x is 2 the (f-g)(x)=0.

When x is zero then (f-g)(x) is negative.

Therefore, the (f-g)(x) is negative in interval ($-\infty,2$).