TRANSFORMATIONS Shifts Stretches And Reflections

TRANSFORMATIONS Shifts Stretches And Reflections

Reflection about the x-axis When a function y = f(x) is multiplied by –1, the which results is f(x) reflected about the x- axis

Reflection about the y-axis When the argument x of a function y = f(x) is multiplied by –1, the which results is f(x) reflected about the y- axis

Vertical Shift • If a positive real number k is added to a function f(x), the graph of the new function f(x)+k is shifted vertically k units K = 3 K= -1

Vertical shifts

Right Horizontal Shift • If the argument x of a function y = f(x) is replaced by x – h for h > 0, the graph of the new function y = f(x – h) is the graph of f(x) shifted horizontally right h units.

Left Horizontal shift • If the argument x of a function y = f(x) is replaced by x + h for h > 0, the graph of the new function y = f(x + h) is the graph of f(x) shifted horizontally left h units. (x + 3)

Combining Vertical and Horizontal Shift

Vertically Stretched and Vertically Compressed Functions When a function f(x) is multiplied by a positive number a, the graph of the new function af(x) is obtained by multplying each y coordinate on the graph of y =f(x) by a.

Vertical Stretch When a function f(x) is multiplied by a positive number athe graph of the new function af(x) is obtained by multplying each y coordinate on the graph of y =f(x) by a. The new graph is a vertically stretched version of a

Vertical Compressions If the graph of a function f(x) is multiplied by a number a so that 0 < a< 1, then the new function af(x) is a vertical compression

Shifts Vertical

Name the function whose graph is given below 1. 2.

TRANSFORMATIONS Shifts Stretches And Reflections