Math 4 Parent Functions Review

Vocabulary flashcards reviewing key parent functions, their equations, domains, ranges, and graphical features.

Extrema

The maximums or minimums of a function, representing its highest or lowest values.

Linear Parent Function

A parent function represented by the equation $y = x$, having a domain and range of $(-\text{infinity}, \text{infinity})$ and no extrema.

Absolute Value Parent Function

A parent function represented by the equation $y = |x|$, which has an absolute minimum at $(0, 0)$.

Absolute Value Range

The range of the absolute value parent function $y = |x|$, defined as $[0, \text{infinity})$.

Quadratic Parent Function

A parent function represented by the equation $y = x^2$, having an absolute minimum at $0$ and a range of $[0, \text{infinity})$.

Quadratic Growth Rate

The rate at which a quadratic function increases, which is quicker than the linear style slope of an absolute value function.

Cubic Parent Function

A parent function represented by the equation $y = x^3$, which increases continuously across its domain without any extrema.

Cubic Domain and Range

The domain and range of the cubic parent function $y = x^3$, both equal to $(-\text{infinity}, \text{infinity})$.

Square Root Parent Function

A parent function represented by the equation $y = \frac{\text{square root}}{\text{x}}$ or $y = \text{sqrt}(x)$, written as $y = \text{sqrt}(x)$ in LaTeX notation.

Square Root Domain

The domain of the square root function $y = \text{sqrt}(x)$, defined as $[0, \text{infinity})$ because square roots of negative numbers are imaginary.

Reciprocal Parent Function

A parent function also referred to as a rational function, represented by the equation $y = \frac{1}{x}$.

Asymptote

A boundary line on a graph that a function gets very close to but cannot touch.

Reciprocal Function Domain

The domain of the reciprocal function $y = \frac{1}{x}$, written as $x \neq 0$ due to a vertical asymptote at the $y$-axis.

Exponential Parent Function

A parent function represented by the equation $y = b^x$ (or $y = 2^x$), where base $b$ can be any constant.

Exponential Function Range

The range of the exponential parent function, defined as $(0, \text{infinity})$ because negative exponents create fractions that approach zero without reaching it.

Exponential Function Y-Intercept

The point where the exponential parent function graph crosses the $y$-axis, located at $(0, 1)$.

Logarithmic Parent Function

A parent function represented by the equation $y = \text{log}(x)$, which serves as the inverse of the exponential function.

Inverse Functions

Pairs of functions whose domains and ranges are flipped relative to each other by switching their $x$ and $y$ values.

Logarithmic Function Domain

The domain of the logarithmic parent function $y = \text{log}(x)$, defined as $(0, \text{infinity})$.

Sinusoidal Functions

Functions that mimic a wave-type behavior, specifically referring to sine and cosine functions.

Sine Parent Function

A wave-pattern parent function represented by the equation $y = \text{sin}(x)$.

Cosine Parent Function

A wave-pattern parent function represented by the equation $y = \text{cos}(x)$.

Sine and Cosine Range

The range for both sine and cosine parent functions, which fluctuates between negative one and positive one, represented as $[-1, 1]$.

Sine Function Y-Intercept

The point where the sine parent function crosses the $y$-axis, located at $(0, 0)$.

Cosine Function Y-Intercept

The point where the cosine parent function crosses the $y$-axis, located at $(0, 1)$.