trigo !!

• half the distance between the maximum value of the function and the minimum value of the function.

  amplitude
• Functions of the form y = f x = a sin bx and y = f x = a cos bx, with

  b > 0, are compressed in the horizontal direction when b > 1 and

  stretched in the horizontal direction when 0 < b < 1.

  period
• A negative sign outside a function −f x results in

  reflection of f(x) about the x-axis.
• A negative sign inside the function f −x results in

  reflection of f(x) about the y-axis.
• Thus the graph of y = a sin bx + k (or y = a cos bx + k) can be

  obtained by shifting the graph of y = a sin bx (or y = a cos bx ) k

  units upward when k > 0 or k units downward when k < 0.

  vertical shifting
• The absolute value of c

  horizontal shifting
• The absolute value of c

  phase shift
• A shift inside the function f x ± c results in a horizontal shift opposite the

  sign of c where c > 0.

  horizontal shifting
• vertical (dashed) line that represents a value of x for which the function is not defined.

  vertical asymptote
• equation of vertical asymptote is of the form ___, where __ is constant.

  x=a, a
• true or false: Some functions like rational functions and logarithmic functions have vertical asymptotes.

  true