Cubic and Cube Root Functions

Cubic/Cube Root Attributes

100

The term for the set of all possible x values for the function f(x)=x³

What is the domain?

200

The range for the parent function f(x)=∛x (and any transformed functions).

What is all real numbers?

300

Instead of a vertex (like a quadratic or absolute value function has), a cubic or a cube root function has this attribute.

What is a point of rotation?

400

A point where the graph crosses or touches the x-axis.

What is an x-intercept?

500

What is the y-intercept of:
f(x)=(⅓(x-3))³-2?
(Hint: Use 0 as your input and simplify)
(Extra hint: an intercept is a point coordinate, not just a number)

What is (0, -3)?

Cubic/Cube Root Transformations

100

If f(x)=∛x, what is the equation for g(x) if it shifts f(x) two units down?

What is ∛(x)-2?

200

If f(x)=x³, how would g(x)=¾(x³)+1 transform f(x)?

What is compress vertically by ¾ AND shift up by 1?

300

If f(x)=x³ and g(x)=-(x+4)³, how has g(x) been transformed from f(x)?

What is reflected vertically and shifted left 4?

400

Write out the equation for g(x) if it transforms f(x)=∛x by stretching vertically by 2, shifting right by 4, and shifting up by 3?

What is g(x)=2∛(x-4)+3?

500

Write down the transformations for g(x)=⅕(-(x-3))³+5

What is vertically compressed by one fifth, reflected horizontally, shifted right 3, and shifted up 5.

Solving Rational Exponents

100

The way we convert the rational exponent into a radical?

What is power over root?

200

If 4(3x-3)^2/3=36.

What is 10?

300

If (2x+3)^4/3-3=13.

What is 5/2?

500

The formula for Meteor Crater in Arizona is d=2∛(V/0.3) and the diameter d of the rim (in meters) relates to the volume V (in cubic meters). If the crater is 1200 meters wide then determine the volume.

What is 64,800,000 m³?

Cubic/Cube Root Equations

100

What is the first step of solving a cubic or cube root equation?

What is isolate the cubic or cube root expression?

200

If 2+∛(x+5)=4

What is x=8?

300

If 4x³=4, find x

What is 1?

400

If 2∛x-3=1, find x.

What is 8?

500

If ½(x-2)³-1=3, what is x?

What is 4?