Question

Given 3x^2+x-4/x-1 what are the domain and range

Answer 1

Answer:

• doman: x ≠ 1
• range: y ≠ 7

Step-by-step explanation:

The domain is the horizontal extent of the graph, the set of x-values for which the function is defined. The range is the vertical extent of the graph, the set of y-values defined by the function.

Simplified

The given function is undefined where its denominator is zero, at x=1. Everywhere else, it can be simplified to ...

  $\dfrac{3x^2+x-4}{x-1}=\dfrac{(x-1)(3x+4)}{(x-1)}=3x+4\quad x\ne 1$

Domain

The simplified function (3x+4) is defined for all values of x except x=1. The simplest description is ...

  x ≠ 1

In interval notation, this is ...

  (-∞, 1) ∪ (1, ∞)

Range

The simplified function is capable of producing all values of y except the one corresponding to x=1: 3(1)+4 = 7. The simplest description is ...

  y ≠ 7

In interval notation, this is ...

  (-∞, 7) ∪ (7, ∞)