The Cubing Function Assignment: E2020 Algebra 2

The graph of the parent function, f(x) = x3, is translated such that the function g(x) = (x - 4)3 - 1 represents the new graph. Which transformations occurred? Horizontal translation: left 1 right 1 left 4 right 4 Vertical translation: up 1 down 1 up 4 down 4

D B

The graph of the parent function f(x) = x3 is translated such that the resulting graph can be represented by the function g(x) = (x - 1)3 + 1. Which is the graph of g(x)?

Graph 1

Which values complete the translated function? g(x) = (x -__ )^3 +__

-2 -4

The function f(x) = -x3 + 2x2 - x + 5 is graphed on a coordinate grid. Which statements accurately describe the end behavior of the graph of the function? As x approaches negative infinity, y approaches positive infinity. As x approaches positive infinity, y approaches negative infinity. As x approaches negative infinity, y approaches positive infinity. As x approaches positive infinity, y approaches positive infinity. As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches negative infinity. As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches positive infinity.

A

The function h(x) = (x - 3)3 + 1 is graphed on a coordinate grid. Which statements about the graph are true? Check all that apply. The domain of the function is all real numbers. The range of the function is all real numbers. The graph is a translation 3 left and 1 up from the function f(x) = x3. The graph crosses the y-axis once. The graph crosses the x-axis three times. The graph increases from negative infinity to positive infinity.

A B D F

Which are solutions to the equation x3 - 5x2 + 2x + 6 = 0? Round each solution to the nearest tenth. Check all that apply. x = -0.9 x = 0.8 x = 1.7 x = 4.2 x = 6.0

A C D

Tia states that the graph of g(x) = (x - 2)3 + 7 is a translation of 2 units to the left and 7 units up from f(x) = x3. Is Tia's description of the translations correct? Explain.

Sample response; No, Tia is not correct. The function g(x) has an h value of 2 and a k value of 7. This would be a horizontal translation of the parent cubic function of 2 units to the right, rather than the left. Tia was correct about the vertical translation of the parent cubic function of 7 units up.

The function f(x) = x3 is translated such that the function describing the translated graph is g(x) = (x + 5)3 + 2. Where is the point (0, 0) for the function f now located on the function g? (__,__ )

-5 2

Which best describes the roots of the function h(x) = x3 - 4x2 - 3x + 18? no real number solutions 1 real number solution 2 real number solutions 3 real number solutions

C

Which is a cubic function? f(x) = 3x + 1 f(x) = 3x2 + x + 2 f(x) = 5x3 + 2x + 1 f(x) = x3 + x4 + 5

C