Determine the values of x, if any, at which the function is discontinuous. at each number where f is discontinuous, state the condition(s) for continuity that are violated. (select all that apply.)f(x) = |x − 1|the function f is discontinuous at x = 1 because f is not defined at x = 1.the function f is discontinuous at x = 1 because lim x → 1 f(x) does not exist. the function f is discontinuous at x = 1 because lim x → 1 f(x) exists, but this limit is not equal to f(1).the function f is continuous everywhere because the three conditions for continuity are satisfied for all values of x.

The function f is continuous everywhere because the three conditions for continuity are satisfied for all values of x.

Step-by-step explanation:

The definition of continuity of a function is:

A function f (x) is continuous at x = a if the following three conditions are met:

We check each condition when x=1

1) f(x)=|x-1| so f(1)=|1-1|=0

The value of f(x) exits when x=1

2) The limit as x approaches 1 of |x-1| can be checked with lateral limits:

=0

=0

Both limits have the same value to the limit exist when x approaches 1.

3) =0=f(1)

The limit as x approaches 1 of f(x) is equal to the value of f(x) exits when x=1

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.