precalc transformations

what is the formula for transformations?

y = af (bx) + c

what does the a represent?

vertical changes

what vertical change occurs when a is > (greater than) 1?

vertical stretch by a factor of # (dilation)

what vertical change occurs when a 0 < a < 1? (a is less than 0 or 1)

vertical compression by a factor of #

what vertical change occurs when a < 0 (less than)

reflection over the x-axis (makes the y-values negative)

what does b represent?

horizontal changes

what occurs when b > 1? (greater than)

horizontal compression by a factor of 1/b

what occurs when 0 < b < 1? (less than)

horizontal stretch by a factor of 1/b

how do you know if there is a reflection over the y-axis?

You know a horizontal change reflects a graph over the y-axis when a negative sign is placed directly inside the function's input (multiplying the x value by -1, changing the coordinate rule from (x,y) to (-x,y)

what does c represent?

vertical translations

what does + c mean?

vertical translation up #

what does - c mean?

vertical translation down #

what is the rule for shifts occuring INSIDE of parentheses

the shift is opposite

f(x-2) —> right 2

f(x+2) —> left 2