Illustration of function transformations such as vertical and horizontal shifts, reflections, and scaling, with labeled graphs and handwritten notes.

- y = f(x) + 3: Shift the graph of f(x) up by 3 units.
- y = f(x + 1): Shift the graph of f(x) left by 1 unit.
- y = -f(x): Reflect the graph of f(x) across the x-axis.
- y = |f(x)|: Reflect all parts of the graph of f(x) that are below the x-axis to above the x-axis.
- (1/2)f(x): Vertically compress the graph of f(x) by a factor of 1/2.
- y = f(-x): Reflect the graph of f(x) across the y-axis.
- y = f(2x): Horizontally compress the graph of f(x) by a factor of 1/2.
- f(x) + 1: Shift the graph of f(x) up by 1 unit.
- y = f(x + 3) - 4: Shift the graph of f(x) left by 3 units and down by 4 units.
- y = 2(f(x - 1)) + 3: Horizontally shift the graph of f(x) right by 1 unit, vertically stretch by a factor of 2, then shift up by 3 units.
- y = f(x - 2): Shift the graph of f(x) right by 2 units.
- y = -2f(x): Vertically stretch the graph of f(x) by a factor of 2 and reflect across the x-axis.
- y = f((1/2)x): Horizontally stretch the graph of f(x) by a factor of 2.
- y = -f(x): Reflect the graph of f(x) across the x-axis.
- y = |f(x)|: Reflect all parts of the graph of f(x) that are below the x-axis to above the x-axis.
- y = f(-x): Reflect the graph of f(x) across the y-axis.
- y = f(x + 2) - 3: Shift the graph of f(x) left by 2 units and down by 3 units.
- y = 2(f((1/2)x)): Horizontally stretch the graph of f(x) by a factor of 2 and vertically stretch by a factor of 2.
- y = -f(x + 1) - 2: Shift the graph of f(x) left by 1 unit, reflect across the x-axis, then shift down by 2 units.