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Rational Functions and Inequalities Quiz

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Rational Functions and Inequalities Quiz

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Questions and Answers

Which expression represents a rational function?

$rac{x-3}{x+5} ext{ is non-negative}$

$rac{2}{x} = x+0$

$f(x) = rac{x+1}{x-3}$ (correct)

$rac{x^{2}-1}{x^{2}+2x+1}$ (correct)

What is the solution for x in the equation $rac{3x+3}{x+4} = rac{x-5}{2}$?

x = 7

x = 12 (correct)

x = 4

x = -17

Which expression signifies a rational inequality?

$y=rac{2}{x+1}$

$rac{1}{3} + rac{1}{x} ext{ is greater than or equal to } 2$ (correct)

$f(x) = rac{x}{x+1}$

$rac{1}{3} + rac{1}{2} = rac{x}{x}$

What is the domain of the function $f(x) = rac{x+8}{5x-7}$?

<p>$ ext{All real numbers, except } x eq rac{5}{7}$ (A)</p> Signup and view all the answers

What is the x-intercept of the function $f(x) = rac{x-1}{x+11}$?

<p>-1 (B)</p> Signup and view all the answers

Flashcards

Rational Function

A function that can be expressed as the quotient of two polynomial functions.

Domain of a rational function

The set of all possible input values (x) for which the function is defined.

Solving rational equations

Finding the value of x that satisfies an equation containing a rational function.

Rational Inequality

An inequality containing a rational function.

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x-intercept of a rational function

The x-value where the graph of the function crosses the x-axis (where y = 0).

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