Parent Functions with Transformations

Linear Function

Parent Absolute Value Function

Parent Quadratic Function

Parent Exponential Function

Parent Square Root Function

y = f(x) + C

Moves the function up C units

y = f(x) - C

Moves the function down C units

y = f(x + C)

Moves the function left C units

y = f(x - C)

Moves the function right C units

y = -f(x)

Reflects the function about x-axis (flips it upside down)

y = 1/4 x^2 transforms to y = 1/4 (x+2)^2 +2

y = x^2 transforms to y = (x-2)^2 +3

y = Cf(x); when C>1

the function narrows (stretches the function in the y-direction)

f(x) = IxI transforms to f(x) = 2 Ix - 2I +1

Square root function reflecting over x axis

y=Cf(x); when 0<C<1

the function widens (compresses the function towards the x-axis)