Math - Shifting Graphs Unit

Quadratic Function

y=x^2

Cubic Function

y=x^3

Square Root Function

y=√x

Cube Root Function

y=^3√x

Absolute Value Function

y=lxl

Reciprocal (Rational) Function

y=1/x

Exponential Function

y=e^x

f(x)

Original Parent Function (x,y)

-f(x)

Reflection over the x-axis (x,-y)

3f(x)

Vertical Stretch by 3 (x,3y)

f(-x)

Reflection over the y-axis (-x,y)

f(3x)

Horizontal shrink by 1/3 (1/3x, y)

f(x+3)

Left by 3 (x-3,y)

f(x-3)

Right by 3 (x+3, y)

f(x)+3

Up by 3 (x, y+3)

f(x)-3

Down by 3 (x,y-3)

(-)a value

(Reflection over x-axis)

Vertical Stretch/Shrink [a>1 stretch / 0<a<1 shrink]

(-)b value

(Reflection over y-axis)

Horizontal Stretch/Shrink [b>1 shrink / 0<b<1 stretch]

(x+c)

Left c

(x-c)

Right c

Grouping symbol outside of b(x+ - c)

Determines Function (square root, cubed, etc)

+d (outside of x value)

Up d

-d (outside of x value)

Down d