Question

The graph of the function f(x) = (x - 3)(x + 1)

Which describes all of the values for which the graph is
positive and decreasing?
.
all real values of x where x < -1
all real values of x where x < 1
all real values of x where 1 all real values of x where x > 3
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Answer 1

The graph is positive and decreasing for all real values of x where x < -1

Explanation:

we have

`f(x)=(x-3)(x+1)`

The function is a vertical parabola open up

The roots (x-intercepts) are x=3 and x=-1

The vertex is the point (1,-4 ) is a minimum

using a graphing tool

see the attached figure

we know that

In the interval (-∞,-1) ---> the function is positive and decreasing

In the interval (-1,1) ---> the function is negative and decreasing

In the interval (1,3) ---> the function is negative and increasing

In the interval (3,∞) ---> the function is positive and increasing

therefore

The graph is positive and decreasing for all real values of x where x < -1