Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing?
(–6, –3)
(–3, –1)
(–3, 0)
(–6, –5)

to know if a function is increasing or decreasing in a given interval [a,b], we will apply the following formula

if the value is positive, then the function is increasing

if the value is negative, then the function is decreasing

case a)

see in the table

substitute in the formula above

> is negative

therefore

in the interval the function is decreasing

case b)

see in the table

substitute in the formula above

> is positive

therefore

in the interval the function is increasing

case c)

see in the table

substitute in the formula above

> is positive

therefore

in the interval the function is increasing

case d)

see in the table

substitute in the formula above

> is negative

therefore

in the interval the function is decreasing

therefore

the answer is

the function is increasing in the intervals