Question

Use the graph shown to find the following
The domain and range of the function
The intercepts if any
Horizontal asymptotes ,if any
Vertical asymptotes, if any
Oblique asymptotes ,if any

Answer 1

Answer:

Step-by-step explanation:

Domain of the function will be,

{x ∈ R | x ≠ -2}

Range of the function is,

{y ∈ R | y ≠ -4}

Intercepts of the function,

Their are no intercepts of the given rational function.

Horizontal asymptotes:

Horizontal line parallel to x-axis representing discontinuity.

y = -4

Vertical asymptotes:

Vertical line parallel to y-axis representing discontinuity.

x = -2

No oblique asymptotes.

Answer 2

A function assigns the value of each element of one set to the other. There are no oblique asymptotes of the given rational function.

What is a function?

A function assigns the value of each element of one set to the other specific element of another set.

The domain of the function

1. The Domain of the function will be {x ∈ R | x ≠ -2}

2.The Range of the function is {y ∈ R | y ≠ -4}

3. As the given function is a rational function, therefore, there are no intercepts of the given function.

4. The Horizontal line parallel to the x-axis represents the discontinuity of the horizontal asymptotes. Therefore, the horizontal asymptotes of the function will lie at y = - 4.

5. The Vertical line parallel to the y-axis represents the discontinuity of the vertical asymptotes. Therefore, the vertical asymptotes of the function will lie at x = -2.

6. There are no oblique asymptotes of the given rational function.

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