Questions: Graph the pair of equations on one set of axes. y=x^3 and y=x^3+5

Transcript text: Graph the pair of equations on one set of axes. $y=x^{3}$ and $y=x^{3}+5$

Solution

Solution Steps

Step 1: Identify the Equations

We are given two equations to graph:

$ y = x^3 $
$ y = x^3 + 5 $

Step 2: Determine the Type of Graph

Both equations are in the form of $ y = f(x) $, which indicates that we will use a Cartesian coordinate system.

Step 3: Determine the Range for the Graph

To effectively display the behavior of the cubic functions, we can choose a reasonable range for $ x $ and $ y $. A typical range for cubic functions might be from -3 to 3 for $ x $ and -10 to 10 for $ y $.

Final Answer

The equations to be graphed are:

$ y = x^3 $
$ y = x^3 + 5 $

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -10, "ymax": 10}, "commands": ["y = x3", "y = x3 + 5"], "latex_expressions": ["$y = x^3$", "$y = x^3 + 5$"]}

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