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Which of the following key features are specific to the graph of a rational function? (Select all that apply.) hole(s) irrational numbers slanted line axis of symmetry slant asymptote

Respuesta :

Rational function:

A rational function is any function which can be defined by a rational fraction,

that is  an algebraic fraction such that both the numerator and the denominator are polynomials

Let's assume

numerator polynomial is p(x)

denominator polynomial is q(x)

so, we can write rational function as

[tex]f(x)=\frac{p(x)}{q(x)}[/tex]

now, we will check each options

option-A:

we know that

we always get hole from rational function only

For exp:

[tex]f(x)=\frac{x^2-9}{x^2-4x+3}[/tex]

Here , hole is at x=3

so, this is TRUE

option-B:

rational functions can not have irrational numbers

because we have both numerator and denominators are polynomial

so, this is FALSE

option-C:

We can get slant asymptote from rational function

For exp:

[tex]f(x)=\frac{x^2-9}{x+3}[/tex]

Here , slant line is y=x-3

so, this is TRUE

option-D:

Rational functions can have axis of symmetry

so, this is TRUE


briannastuck

Answer:

Holes

Slant Asymptote

 

Step-by-step explanation:

The graph of a rational function requires that we examine new features such as point discontinuity (holes), and a slant asymptote.

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