Transformations of Graphs

Vocabulary flashcards covering function graph transformations including shifts, reflections, stretches, and shrinks.

Transformation $y = f(x) + c$ ($c > 0$)

Vertical shift $c$ units upward (add $c$ to each y-coordinate), transforming $(x, y)$ to $(x, y + c)$.

Transformation $y = f(x) - c$ ($c > 0$)

Vertical shift $c$ units downward (subtract $c$ from each y-coordinate), transforming $(x, y)$ to $(x, y - c)$.

Transformation $y = f(x - c)$ ($c > 0$)

Horizontal shift $c$ units to the right (add $c$ to each x-coordinate), transforming $(x, y)$ to $(x + c, y)$.

Transformation $y = f(x + c)$ ($c > 0$)

Horizontal shift $c$ units to the left (subtract $c$ from each x-coordinate), transforming $(x, y)$ to $(x - c, y)$.

Transformation $y = -f(x)$

Reflect the graph about the x-axis (replace $y$ by $-y$), transforming $(x, y)$ to $(x, -y)$.

Transformation $y = f(-x)$

Reflect the graph about the y-axis (replace $x$ by $-x$), transforming $(x, y)$ to $(-x, y)$.

Transformation $y = c \times f(x)$ ($c > 1$)

Vertically stretch the graph by a factor of $c$ (multiply each y-coordinate by $c$), transforming $(x, y)$ to $(x, c \times y)$.

Transformation $y = c \times f(x)$ ($0 < c < 1$)

Vertically shrink the graph by a factor of $c$ (multiply each y-coordinate by $c$), transforming $(x, y)$ to $(x, c \times y)$.

Transformation $y = f(c \times x)$ ($c > 1$)

Horizontally shrink the graph by a factor of $c$ (divide each x-coordinate by $c$), transforming $(x, y)$ to $(\frac{x}{c}, y)$.

Transformation $y = f(c \times x)$ ($0 < c < 1$)

Horizontally stretch the graph by a factor of $c$ (divide each x-coordinate by $c$), transforming $(x, y)$ to $(\frac{x}{c}, y)$.