Lesson 4: 5-5 Graphing Cube Root Fuctions

What is the domain and range of a cube root function?
How do you find the point where the curvature of the cube root function changes, the inflection point, if the function has been transformed in the plane?
Is a cube root function that has been transformed in the plane also a function? Explain.

cube root function
inflection point

F.IF.4 For a function that models a relationship between two quantities, interpret dey features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.IF.7b Graph square root, cube root, and piecewise defined functions, including step function and absolute value functions
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx) and f(x+k) for specific values of k; find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

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Cube root functions are a type of radical function that can be useful when solving formulas that involve the cube of a variable for the variable. For example, to find the radiusr of a sphere if you know the volume, V, rewrite V=4/3pir^3 as a function of V, or r(V)=(3V/(4pi)^(1/3)

A giraffe is a mammal that has an average life span of 25 years in the wild. It can range in height from 4 to 6 meters, and it can weigh from 794 to 1270 kilograms. The height h in meters of some small giraffes weighing x kilograms can be approximated by the cube root function h(x)=.45(x)^(1/3)

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Ask expert learners How is the graph of y=(x-1)^(1/3)-4 related to graph of y=(x+4)^3+1?

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