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).

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation:

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation: