Unit 1 Functions and Transformations Flashcards

Vocabulary practice flashcards generated from Unit 1 lecture notes covering parent function terminology and function transformation rules.

Domain

Total possible set of $x$-values.

Range

Total possible set of $y$-values.

Asymptote

A line which a function approaches but never touches.

End Behavior

Describes whether the domain and range increase or decrease at the ends of a function.

Absolute Maximum

The highest point in a function.

Absolute Minimum

The lowest point in a function.

Relative Maximum

The highest point in a region of a function.

Relative Minimum

The lowest point in a region of a function.

Quadratic Parent Function

$$F(x) = x^2$$

Absolute Value Parent Function

$$f(x) = |x|$$

Vertical Dilation

Represented by $g(x) = a \times f(x)$, where $0 < |a| < 1$ produces a vertical compression and $|a| > 1$ produces a vertical stretch.

Horizontal Dilation

Represented by $g(x) = f(b(x))$, where $|b| > 1$ produces a horizontal compression and $0 < |b| < 1$ produces a horizontal stretch by a factor of $\frac{1}{|b|}$.

Vertical Reflection

Represented by $g(x) = -f(x)$ or $-a$.

Horizontal Reflection

Represented by $g(x) = f(-x)$ or $-b$.

Vertical Translation

Represented by $g(x) = f(x) + k$.

Horizontal Translation

Represented by $g(x) = f(x + h)$, where $+$ shifts to the left and $-$ shifts to the right.

Vertex Form

$$g(x) = a \times f(b(x + h)) + k$$

Transformation Steps

1. Name the parent function
2. Write $g(x)$ in vertex form
3. Apply transformations

Order of Transformations

1. Reflections
2. Dilations
3. Translations