Question

The piecewise function f(x) has opposite expressions.

Answer 1

Answer:

We will choose option 3.

Step-by-step explanation:

The piecewise function f(x) has the following definition :

f(x) = 2x - 1, when x < 0 ........... (1)

f(x) = 0, when x = 0 and ........... (2)

f(x) = - 2x + 1, when x > 0 ........... (3)

Now, on a coordinate plane, this piecewise function has 2 lines. The first line goes up from (-2,-5) to a closed circle at (0,-1). The second line has a closed circle at (0, 1) and goes down through (2,-3).

This is because, the point (-2,-5) satisfies equation (1) and as x tends to -0 from equation (1), f(x) tends to -1.

Again the point (2,-3) satisfies equation (3) and as x tends to +0 from equation (3), f(x) tends to 1.

Hence, we will choose option 3. (Answer)

Answer 2

Answer:

On a coordinate plane, a piecewise function has 2 lines. The first line goes up from (negative 2, negative 5) to a closed circle at (0, -1). The second line has a closed circle at (0, 1) and goes down through (2, -3).

Step-by-step explanation:

Let's visualize this piecewise function, or function by parts.

$f(x)=\left\{\begin{matrix}2x-1,&x0 \end{matrix}\right.$

Piecewise function is a function where each piece of function describes a behavior, i.e. returning another value depending on the input value.

Piecewise functions are pretty useful when we study limits.

According to the description given, the 3rd. option matches the graph. The second behavior (0,0) we'll describe it as a point.