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How do you graph #y = | x^3 - 1 |#?

Answer 1

Eva Abramson

graph{|x^3-1| [-5, 5, -5, 5]}

Firstly, understand a general cubic graph,

#y=x^3# graph{y=x^3 [-5, 5, -5, 5]}

Secondly, know that #c=-1#, where #c# is the y-intercept, so move the graph down to #-1#.

#y=x^3-1# graph{y=x^3-1 [-5, 5, -5, 5]}

Thirdly, by inserting the modulus function, any value that is negative will be positive, so #y>=0#, hence reflecting anything below the x-axis up.

#y=|x^3-1|# graph{|x^3-1| [-5, 5, -5, 5]}

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Answer 2

Jace Anderson

To graph the function ( y = |x^3 - 1| ):

Identify critical points where the expression inside the absolute value changes sign. In this case, solve ( x^3 - 1 = 0 ) to find ( x = 1 ).
Plot the critical point(s) on the x-axis.
Determine the behavior of the function on different intervals:
- For ( x < 1 ): Substitute values less than 1 into ( x^3 - 1 ) and take the absolute value.
- For ( x > 1 ): Substitute values greater than 1 into ( x^3 - 1 ) and take the absolute value.
Plot the points obtained from step 3 to sketch the graph of the function.
Remember that the graph will reflect above the x-axis due to the absolute value.
Connect the points smoothly to form the graph of ( y = |x^3 - 1| ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.