alg 2 transformation

isolate the absolute value |x|

step 1 solving absolute value equations

separate into two equations, one positive answer & one negative answer

step 2 solving absolute value equations

solve equations/combine like terms

step 3 solving absolute value equations

check solutions if there are two x values in the equation

step 4 solving absolute value equations

0 < b < 1 ( y = ± a * f (± b ( x - h ) ) + k )

horizontal stretch by factor of 1/b

b > 1 ( y = ± a * f (± b ( x - h ) ) + k )

horizontal compression by factor of 1/b

positive f(± x) value ( y = ± a * f (± b ( x - h ) ) + k )

no reflection across the y-axis

negative f(± x) value ( y = ± a * f (± b ( x - h ) ) + k )

reflection across the y-axis

positive h value ( y = ± a * f (± b ( x - h ) ) + k )

horizontal shift leftof the graph by h units.

negative h value ( y = ± a * f (± b ( x - h ) ) + k )

horizontal shift right of the graph by h units.

positive ± f(x) value ( y = ± a * f (± b ( x - h ) ) + k )

no reflection across the x-axis

negative ± f(x) value ( y = ± a * f (± b ( x - h ) ) + k )

reflection across the x-axis

a > 1 ( y = ± a * f (± b ( x - h ) ) + k )

vertical stretch

0 < a < 1 ( y = ± a * f (± b ( x - h ) ) + k )

vertical compression

positive k value ( y = ± a * f (± b ( x - h ) ) + k )

vertical shift up

negative k value ( y = ± a * f (± b ( x - h ) ) + k )

vertical shift down

inversely affects x-values

inside of parentheses

obviously affects y-values

outside of the parentheses

f (x) = x

linear equation

f (x) = x²

quadratic equation

f (x) = x³

cubic equation

f (x) = B^x

exponential function, where the base B is a constant.

f (x) = |x|

absolute value equation

f (x) = √x

square root equations

f (x) = ³√x

cube root equation

f (x) = log_Bx

logarithmic equation