Homework Help

Which of the  statements is true regarding the function‘s intervals of increase and...

user profile pic

foxwit | Student, Undergraduate | (Level 1) Salutatorian

Posted July 18, 2013 at 10:20 PM via web

dislike 1 like

Which of the  statements is true regarding the function‘s intervals of increase and decrease?

a)

The function is decreasing when x< 4 and increasing when x> 4

b)

The function is always decreasing

c)

The function is always increasing

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

1 Answer | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 19, 2013 at 5:58 PM (Answer #1)

dislike 1 like

The image provided by the problem shows that the graph of the function intersects x axis at `x = 4` , hence, the equation of the function has a real solution at `x= 4` .

You may notice that the graph of the function goes down along a vertical line `x = 3` , parallel to y axis, hence, the graph of the function has a vertical asymptote `x = 3.`

You may notice that the the larger the x values are, the larger the y values are, hence, using the definition of increasing function `x_1<x_2 => y_1<y_2` , yields that the function is always increasing.

Hence, since the function is always increasing, you need to select the answer c).

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes