COPY: Rational Functions and Their Graphs

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Which of the following represents a rational function?

$k(x) = 3x^3 - 5x$

$h(x) = x^2$

$g(x) = \frac{1}{x + 1}$ (correct)

$f(x) = 2x + 1$

The function $f(x) = \frac{1}{x}$ has a domain that includes 0.

False

What is the domain of the function $g(x) = \frac{1}{x + 1}$?

x = {x | x ≠ -1}

The range of the function $f(x) = \frac{x}{x - 1}$ is __________.

y = {y | y ≠ 1} Signup and view all the answers

Match the following functions with their corresponding domain:

$f(x) = \frac{1}{x}$ = $x ≠ 0 $g(x) = \frac{1}{x + 1}$ = $x ≠ -1 $F(x) = \frac{x}{x - 1}$ = $x ≠ 1 $G(x) = \frac{2x}{x + 3}$ = $x ≠ -3 Signup and view all the answers

What is the common feature of the graphs of the functions $f(x)$ and $g(x)$?

They do not touch the x-axis. Signup and view all the answers

Identify the range of the function $f(x) = \frac{1}{x}$.

y = {y | y ≠ 0} Signup and view all the answers

For the function $G(x) = \frac{2x}{x + 3}$, the value that x cannot take is __________.

-3 Signup and view all the answers

What is the vertical asymptote of the function $g(x) = \frac{2x - 1}{x + 3}$?

x = -3 Signup and view all the answers

The horizontal asymptote of the function $g(x) = \frac{2x - 1}{x + 3}$ is y = 2.

True Signup and view all the answers

Identify one point on the graph of the function $g(x) = \frac{2x - 1}{x + 3}$ when x = -5.

11/2 Signup and view all the answers

The equation of the horizontal asymptote is __________.

y = 2 Signup and view all the answers

Match the following functions with their descriptions:

f(x) = \frac{x - 2}{x + 5} = Rational function with a linear numerator and denominator F(x) = \frac{2 - 3x}{x - 3} = Rational function decreasing as x increases g(x) = \frac{1 - x}{x + 4} = Rational function with a negative slope G(x) = \frac{3x}{x - 3} = Rational function with a vertical asymptote at x = 3 Signup and view all the answers

What is the domain of the function defined by $f(x) = \frac{x - 2}{x - 3}$?

x = {x | x ≠ 3} Signup and view all the answers

The range of the function $g(x) = \frac{2x - 1}{x + 3}$ includes the value 2.

False Signup and view all the answers

Identify the vertical asymptote for the function $g(x) = \frac{2x - 1}{x + 3}$.

x = -3 Signup and view all the answers

The vertical asymptote of the function $f(x) = \frac{x - 2}{x - 3}$ is __________.

x = 3 Signup and view all the answers

Match the following asymptotes with their corresponding functions:

$f(x) = \frac{x - 2}{x - 3}$ = Vertical Asymptote: x = 3 $g(x) = \frac{2x - 1}{x + 3}$ = Vertical Asymptote: x = -3 $h(x) = \frac{x + 1}{x - 4}$ = Vertical Asymptote: x = 4 $k(x) = \frac{x^2 - 1}{x + 2}$ = Vertical Asymptote: x = -2 Signup and view all the answers