Task Sets: Graph rational functions - Common Core Math - HS Functions

Concepts

For $f(x) = \dfrac{(x-2)(x+3)}{(x-2)(x-5)}$ , what happens at $x = 2$ ?

There is a vertical asymptote at $x = 2$ .

There is a zero (x-intercept) at $x = 2$ .

There is a removable discontinuity (hole) at $x = 2$ .

The function is defined and continuous at $x = 2$ .

Which rule correctly determines the horizontal asymptote of a rational
function $\dfrac{p(x)}{q(x)}$ when $\deg(p) = \deg(q)$ ?

The horizontal asymptote is $y = 0$ .

The horizontal asymptote is $y = \dfrac{\text{leading coefficient of } p}{\text{leading coefficient of } q}$ .

There is no horizontal asymptote.

The horizontal asymptote is $y = 1$ .

For $h(x) = \dfrac{x^3 + 1}{x^2 - 4}$ , how many horizontal asymptotes
does the graph have? Enter 0 or 1.

Procedures

For $f(x) = \dfrac{x^2 - 9}{x^2 - x - 6}$ , identify all x-intercepts
(zeros). Select the correct list.

$x = 3$ and $x = -3$

$x = -3$ only

$x = 3$ only

No x-intercepts

Find the x-coordinate of the hole in the graph of
$g(x) = \dfrac{x^2 - 4}{x - 2}$ .
Enter the x-value only.

For $f(x) = \dfrac{3x - 6}{x^2 - 3x - 10}$ , find all vertical
asymptotes. Enter the larger x-value of the two vertical asymptotes.

Determine the horizontal asymptote of
$f(x) = \dfrac{4x^2 - 1}{2x^2 + 3x}$ .
Enter the y-value of the horizontal asymptote as a fraction or decimal.
(Example: enter $2$ for $y = 2$ .)

HSF.IF.C.7.d Tutor Intake — Rational Function Key Features

Concepts

Procedures