5.06 Sketching polynomials
Interactive practice questions
By considering the graph of $y=x^3$y=x3, determine the following:
A Cartesian plane with the $x$x-axis ranging from $-10$−10 to $10$10 and the $y$y-axis ranging from $-40$−40 to $40$40. The $x$x-axis is marked and labeled with integers at major intervals of $2$2 units and minor intervals of $1$1 unit. The $y$y-axis is marked and labeled with integers at major intervals of $10$10 units and minor intervals of $5$5 units. The graph of $y=x^3$y=x3 is plotted on the Cartesian plane. The curve moves upward from left to right. From the left, the curve moves upward steeply until it approaches the origin $\left(0,0\right)$(0,0), where it becomes gradually less steep. As it extends to the right from the origin, the curve moves upward steeply again, becoming steeper as it moves further away from the origin.
As $x$x becomes larger in the positive direction (ie $x$x approaches infinity), what happens to the corresponding $y$y-values?
they approach zero
they become very large in the positive direction
they become very large in the negative direction
As $x$x becomes larger in the negative direction (ie $x$x approaches negative infinity), what happens to the corresponding $y$y-values?
they become very large in the positive direction
they approach zero
they become very large in the negative direction
Does the graphed function have an even or odd power?
Consider the graph of the function $y=x^3$y=x3.
Fill in the gaps to complete the statement.
Consider the cubic function $y=-x^3$y=−x3