Algebraic Functions and Graph Properties Vocabulary

Vocabulary flashcards covering rational functions, vertical and horizontal asymptotes, graph symmetry, and practical variable constraints based on the lecture.

Number of Items ($x$)

A contextual variable representing physical units sold, which cannot logically be negative or a non-integer decimal.

Maximum Profit

The peak output value on a symmetric profit graph, located precisely at the midpoint between symmetric zero-profit points.

Symmetric Points

Pairs of input values (such as $30$ and $80$) that lie equidistant from the central axis or maximum point (such as $55$) on a symmetric graph.

Rational Function

A ratio of two polynomials where the denominator contains a variable polynomial rather than just a constant number.

Vertical Asymptote

A vertical line with an equation of the form $x = c$, found by setting the denominator of a rational function equal to zero.

Horizontal Asymptote

A horizontal line with an equation of the form $y = c$, found by taking the ratio of the coefficients of the highest power of $x$ in the numerator and denominator.

No $x$-intercept

A property of a graph indicating that there are no real solutions, meaning the curve never crosses the x-axis.

$y$-intercept

The point where a graph crosses the y-axis, calculated by evaluating the function when $x = 0$.