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# Shifting Reflecting Sketching Graph

Graphs of Commonly Used Functions in Algebra

a.) Constant Function b.) Identity Function c.) Absolute Value Function d.) Square Root Function e.) Quadratic Function f.) Cubic Function Most graphs of functions can be made by transforming (shifting, stretching, shrinking, reflecting) or
combining these common graphs.

Vertical and Horizontal Shifts

Let c be a positive real number. Vertical and horizontal shifts in the graphs of y = f(x) are represented
as follows:

1.) Vertical shift c units upward -> h(x) = f(x) + c
2.) Vertical shift c units downward -> h(x) = f(x) – c
3.) Horizontal shift c units to the right -> h(x) = f(x – c)
4.) Horizontal shift c units to the left -> h(x) = f(x + c)

Reflections in the Coordinate Axes

Reflections in the coordinate axes of the graph of y = f(x) are represented as follows:
1.) Reflection in the x-axis -> h(x) = -f(x)
2.) Reflection in the y-axis -> h(x) = f(-x)

Nonrigid Transformations

1.) A vertical stretch in the graph -> y = cf(x) where c > 1
2.) A vertical shrink in the graph -> y = cf(x) where 0 < c < 1
3.) A horizontal shrink in the graph -> y = f(cx) where c > 1
4.) A horizontal stretch in the graph -> y = f(cx) where 0 < c < 1

Vertical Shifts in the Graph of f (x) = x^2 . Horizontal Shifts in the Graph of f (x) = x^2 . Reflection in the x-axis of the Graph of f (x) = x^2 . Reflection in the y-axis of the Graph of  Vertical Stretches and Shrinks of the Graph of f (x) = x^2 . Horizontal Stretches and Shrinks of the Graph of f (x) = x^2 . Identify the common function and describe the transformation shown in the graph. Write an
equation for the graphed function.
a.) Solution:

b.) Solution: