Parent and Periodic Functions

0.0(0)
Studied by 0 people
call kaiCall Kai
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
GameKnowt Play
Card Sorting

1/10

flashcard set

Earn XP

Description and Tags

Vocabulary review covering parent function equations, domains, ranges, and fundamental features of periodic functions.

11 Terms

1
New cards

Linear Parent Function

A parent function with the equation f(x)=xf(x) = x, domain D={x∈R}D = \{x \in \mathbb{R}\}, and range R={y∈R}R = \{y \in \mathbb{R}\}.

<p>A parent function with the equation $$f(x) = x$$, domain $$D = \{x \in \mathbb{R}\}$$, and range $$R = \{y \in \mathbb{R}\}$$.</p>
2
New cards

Quadratic Parent Function

A parent function with the equation f(x)=x2f(x) = x^2, domain D={x∈R}D = \{x \in \mathbb{R}\}, and range R={y∈R∣y≥0}R = \{y \in \mathbb{R} \mid y \ge 0\}.

<p>A parent function with the equation $$f(x) = x^2$$, domain $$D = \{x \in \mathbb{R}\}$$, and range $$R = \{y \in \mathbb{R} \mid y \ge 0\}$$.</p>
3
New cards

Square Root Parent Function

A parent function with the equation f(x)=xf(x) = \sqrt{x}, domain D={x∈R∣x≥0}D = \{x \in \mathbb{R} \mid x \ge 0\}, and range R={y∈R∣y≥0}R = \{y \in \mathbb{R} \mid y \ge 0\}.

<p>A parent function with the equation $$f(x) = \sqrt{x}$$, domain $$D = \{x \in \mathbb{R} \mid x \ge 0\}$$, and range $$R = \{y \in \mathbb{R} \mid y \ge 0\}$$.</p>
4
New cards

Reciprocal Parent Function

A parent function with the equation f(x)=1xf(x) = \frac{1}{x}, domain D={x∈R∣x≠0}D = \{x \in \mathbb{R} \mid x \ne 0\}, and range R={y∈R∣y≠0}R = \{y \in \mathbb{R} \mid y \ne 0\}.

<p>A parent function with the equation $$f(x) = \frac{1}{x}$$, domain $$D = \{x \in \mathbb{R} \mid x \ne 0\}$$, and range $$R = \{y \in \mathbb{R} \mid y \ne 0\}$$.</p>
5
New cards

Absolute Value Parent Function

A parent function with the equation f(x)=∣x∣f(x) = |x|, domain D={x∈R}D = \{x \in \mathbb{R}\}, and range R={y∈R∣y≥0}R = \{y \in \mathbb{R} \mid y \ge 0\}.

<p>A parent function with the equation $$f(x) = |x|$$, domain $$D = \{x \in \mathbb{R}\}$$, and range $$R = \{y \in \mathbb{R} \mid y \ge 0\}$$.</p>
6
New cards

Exponential Parent Function

A parent function with the equation f(x)=bxf(x) = b^x (where bb is any number), domain D={x∈R}D = \{x \in \mathbb{R}\}, and range R={y∈R∣y>0}R = \{y \in \mathbb{R} \mid y > 0\}.

<p>A parent function with the equation $$f(x) = b^x$$ (where $$b$$ is any number), domain $$D = \{x \in \mathbb{R}\}$$, and range $$R = \{y \in \mathbb{R} \mid y > 0\}$$.</p>
7
New cards

Peak

The maximum value of a periodic function.

8
New cards

Trough

The minimum value of a periodic function.

9
New cards

Midline / Equation of the Axis

The central horizontal line of a periodic function, calculated as max+min2\frac{\text{max} + \text{min}}{2}.

10
New cards

Period

How long one cycle takes in a periodic function.

11
New cards

Amplitude

The distance between the middle and the maximum or minimum of a periodic function, calculated as max−min2\frac{\text{max} - \text{min}}{2}.