Parent Functions and Transformations Vocabulary

Vocabulary flashcards generated from the notes on parent functions, function families, and various graph transformations.

Parent Function

The most basic function in a family of functions.

Transformation

A change in the size, shape, position, or orientation of a graph.

Translation

A transformation that shifts a graph horizontally and/or vertically but does not change its size, shape, or orientation.

Reflection

A transformation that flips a graph over a line called the line of reflection.

Constant Parent Function

The function $f(x) = 1$ with a domain of all real numbers and a range of $y = 1$.

Linear Parent Function

The function $f(x) = x$ with a domain of all real numbers and a range of all real numbers.

Absolute Value Parent Function

The function $f(x) = |x|$ with a domain of all real numbers and a range of $y \frac{1}{2} 0$ (or $y \neq 0$).

Quadratic Parent Function

The function $f(x) = x^2$ with a domain of all real numbers and a range of $y \frac{1}{2} 0$.

Horizontal Translation

The graph of $f(x - h)$ where $h \neq 0$; subtracting $h$ from the inputs before evaluating shifts the graph left when $h < 0$ and right when $h > 0$.

Vertical Translation

The graph of $y = f(x) + k$ where $k \neq 0$; adding $k$ to the outputs shifts the graph down when $k < 0$ and up when $k > 0$.

Reflection in the x-axis

The graph of $y = -f(x)$, which multiplies the outputs of $f(x)$ by $-1$.

Reflection in the y-axis

The graph of $y = f(-x)$, which multiplies the inputs of $f(x)$ by $-1$.

Horizontal Stretch

The graph of $f(ax)$ where $0 < a < 1$; multiplying the inputs by $a$ stretches the graph horizontally away from the y-axis while keeping the y-intercept the same.

Horizontal Shrink

The graph of $f(ax)$ where $a > 1$; multiplying the inputs by $a$ shrinks the graph horizontally towards the y-axis while keeping the y-intercept the same.

Vertical Stretch

The graph of $y = a \times f(x)$ where $a > 1$; multiplying the outputs by $a$ stretches the graph vertically away from the x-axis while keeping the x-intercept the same.

Vertical Shrink

The graph of $y = a \times f(x)$ where $0 < a < 1$; multiplying the outputs by $a$ shrinks the graph vertically towards the x-axis while keeping the x-intercept the same.