Which are points on the graph of y = 1.5 + ⌈x⌉? check all that apply. a. (–4.5, –2.5) b. (–1.5, 0) c. (–0.8, 0.5) d. (1.3, 3.5) e. (4.5, 6) f. (7.9, 9.5)

Option A,D and F

Step-by-step explanation:

Given : Function

To find : Which are points lie on the graph of given function?

Solution :          

To determine the points lie on the graph,

First we graphed the given function

In the function, ⌈x⌉ means the ceiling of x, i.e. the smallest integer greater than or equal to x.

Refer the attached figure below.

Now, We mark all the points mention in question.

We note the point line on the ceiling x are A(-4.5, -2.5), D(1.3, 3.5) and F(7.9, 9.5).

Therefore, The required result is Option A,D and F.

Hello from MrBillDoesMath!

#11. Your choice, 3x + 1 <= 4, is correct

#13 Your choice, 8p +5 > 21. is correct

Discussion:

#11,    Let's explore:  3x + 1 <= 4

3x + 1 <= 4 =>

3x + 1 -1 <= 4 - 1  =>                         (subtract 1 from both sides)

3x <= 3 =>

x <=1

which matches the red line segment shown.  In the diagram, the point x = 1 is included (a solid dot) as in our solution x <=1.

#13. The second radio button,  the one you selected, is correct. Let's explore:

8p + 5 > 21 =>

8p + 5 -5 > 21 - 5                    (subtract 5 from both sides)

8p > 16                                    (as 21-5 = 16)

p > 2                                        (divide both sides by 8)

Note that this solution, like the graph ("open circle" at 2) does NOT include the point p = 2

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!