Which points lie on the graph of the function f(x) = ⌈x⌉ + 2? check all that apply.
a. (–5.5, –4)
b. (–3.8, –2)
c. (–1.1, 1)
d. (–0.9, 2)
e. (2.2, 5)
f. (4.7, 6)

Only the points C, D and F lie on the graph

Step-by-step explanation:

Given : f(x) = [ x ] + 2

[ x ] is ceiling function which results the least integer greater than or equal to x

The point which lie on the graph of f(x) must satisfy the condition of the function.

A. (–5.5, –4)

f(-5.5) = [-5.5] + 2 = -5 + 2 = -3 ≠ -4

So, the point does not lie on the graph of the function.

B. (–3.8, –2)

f(-3.8) = [-3.8] + 2 = -3 + 2 = -1 ≠ -2

So, the point does not lie on the graph of the function.

C. (–1.1, 1)

f(-1.1) = [ -1.1] + 2 = -1 + 2 = 1 = 1

So, the point lie on the graph of the function.

D. (–0.9, 2)

f(-0.9) = [-0.9 ] + 2 = 0 + 2 = 2 = 2

So, the point lie on the graph of the function.

E. (2.2, 5)

f(2.2) = [2.2] + 2 = 2 + 2 = 4 ≠ 5

So, the point does not lie on the graph of the function.

F. (4.7, 6)

f(4.7) = [4.7] + 2 = 4 + 2 = 6 = 6

So, the point lie on the graph of the function.

Hence, only the points C, D and F lie on the graph as only these points satisfy the given equation of the function f(x).

the answer is 62.8 cubic units