Transformation of a function

Definition

A transformation of a function involves shifting, stretching, compressing, or reflecting its graph. These modifications alter the original function's appearance but not its basic shape.

5 Must Know Facts For Your Next Test

1. Vertical shifts occur when you add or subtract a constant from the function: $f(x) + c$ or $f(x) - c$.
2. Horizontal shifts happen when you add or subtract a constant inside the argument: $f(x+c)$ or $f(x-c)$.
3. Vertical stretching and compressing are achieved by multiplying the function by a constant: $af(x)$ where $a > 1$ stretches and $0 < a < 1$ compresses.
4. Horizontal stretching and compressing occur by modifying the input variable with a constant factor: $f(bx)$ where $0 < b < 1$ stretches and $b > 1$ compresses.
5. Reflection across the x-axis is done by negating the function: $-f(x)$, while reflection across the y-axis is performed by negating the input variable: $f(-x)$.

Review Questions

Related terms

Vertical Shift:

A transformation that moves the graph of a function up or down without changing its shape.

Horizontal Shift:

A transformation that moves the graph of a function left or right without altering its shape.

Reflection:

$A transformation that flips the graph of a function over an axis.$