write an equation for the shape of f(x)=x^(3) but moved two units to the left, five units up, and reflected in the y-axis

Answer 1

A transformation left 2 units looks like this: (x+2)

For a transformation up 5, you just add 5 to the end of the equation.

Reflected over the y-axis is also called a horizontal reflection. For this, you place a negative sign in front of x inside parenthesis. (Outside of parenthesis is a vertical transformation).

After these 3 transformations, the equation is

y = (-x+2)³ + 5

Answer 2

Start with base equation y = x³

Shift to left means adding shift to x before function operates: y = (x+2)³

Shift upwards means adding to previous y value: y = (x+2)³ + 5

Reflecting about y axis results from plugging in -x for x : y = (2-x)³ + 5

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