LCPS Algebra 2 Unit 2 Analyzing and Describing Graphs of Functions

A set of vocabulary flashcards identifying and describing key parent functions, their equations, graphical characteristics, and tables of values based on the Unit 2 assessment material.

Quadratic Parent Function

The most basic quadratic function, represented equationally as $f(x) = x^2$, whose graph is a symmetric U-shaped curve called a parabola with a vertex at $(0,0)$.

Square Root Parent Function

The function $f(x) = \sqrt{x}$, defined for $x \ge 0$, whose graph originates at $(0,0)$ and extends into Quadrant I as a half-sideways parabola.

Rational Parent Function

The reciprocal function $f(x) = \frac{1}{x}$, characterized by two hyperbolic branches in Quadrants I and III with asymptotes at $x = 0$ and $y = 0$.

Cube Root Parent Function

The function $f(x) = \sqrt[3]{x}$, whose graph forms an S-shaped curve passing through the origin $(0,0)$, extending across all real numbers for both domain and range.

Logarithmic Parent Function

A function of the form $f(x) = \log_b(x)$, featuring a vertical asymptote, an x-intercept at $(1,0)$, and slow continuous growth as $x$ increases.

Cubic Parent Function

The function $f(x) = x^3$, whose graph is an S-curve centered at the origin $(0,0)$ that extends infinitely upward into Quadrant I and downward into Quadrant III.

Absolute Value Parent Function

The function $f(x) = |x|$, whose graph forms a symmetric V-shape opening upward with its vertex at $(0,0)$.

Exponential Parent Function

A function of the form $f(x) = b^x$ (where $b > 0$ and $b \neq 1$), characterized by a horizontal asymptote and rapid growth or decay.

Exponential vs. Logarithmic Graph Relationship

Exponential functions (such as Graph A) exhibit rapid vertical growth with a horizontal asymptote, whereas logarithmic functions (such as Graph B) grow slowly with a vertical asymptote; the two functions are inverse functions of each other.

Linear Parent Function

The most basic linear function $f(x) = x$, represented graphically as a straight line passing through the origin $(0,0)$ with a slope of $1$.

Table of Values for Rational Function $f(x) = \frac{1}{x}$

A set of ordered pairs where output values $f(x)$ are the multiplicative inverses of input values $x$, such as $(-4, -\frac{1}{4})$, $(-2, -\frac{1}{2})$, and $(6, \frac{1}{6})$.

Table of Values for Square Root Function $f(x) = \sqrt{x}$

A set of ordered pairs mapping non-negative square input values $x$ to their principal square roots $f(x)$, such as $(0, 0)$, $(1, 1)$, $(4, 2)$, and $(9, 3)$.

Table of Values for Cube Root Function $f(x) = \sqrt[3]{x}$

A set of ordered pairs mapping perfect cube inputs $x$ across negative and positive numbers to their cube roots $f(x)$, such as $(-8, -2)$, $(0, 0)$, $(1, 1)$, and $(27, 3)$.