which is the graph of the step function f(x)?

f(x) = {-1x< -1} 0-1< x< 1 1x> 1



image for option 1

The graph of the step function f(x) is represented by the 2nd graph.

Step-by-step explanation:

We are given the step function,

.

So, from the options, we see that,

In 1st graph, the conditions and is not satisfied.

In 3rd graph, the points -1,0,1 are included, which is not correct.

In 4th graph, and is not satisfied.

Thus, we have,

The graph of the step function f(x) is represented by the 2nd graph as shown below.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

i dont know

step-by-step explanation: