Understanding Cubic Functions with Desmos

This video tutorial demonstrates how to graph a cubic function using Desmos, identify where the function is increasing or decreasing, and determine any relative extrema. It provides a step-by-step guide on entering the function, adjusting the graph view, and analyzing key points such as intercepts, maxima, and minima. The tutorial also explains how to interpret the graph to understand the function's behavior over different intervals.

What does it mean for a function to be increasing on a graph?

• The graph is oscillating.

• The graph is flat.

• The graph is moving uphill.

• The graph is moving downhill.

What is a relative maximum in the context of a graph?

• A point where the graph is flat.

• A point where the graph is at its lowest.

• A point where the graph changes from decreasing to increasing.

• A point where the graph changes from increasing to decreasing.

Which key is used to enter an exponent in Desmos?

• The division key.

• The exponent key (a^b).

• The minus key.

• The plus key.

How can you adjust the view of the graph in Desmos?

• By changing the font size.

• By clicking and dragging the graph.

• By rotating the graph.

• By changing the color of the graph.

What should you do if the graph view is not ideal?

• Change the background color.

• Change the graph type.

• Adjust the x and y axis values.

• Restart Desmos.

What does the ordered pair (1, 30) represent on the graph?

• A y-intercept.

• A relative minimum.

• A relative maximum.

• An x-intercept.

What is the significance of the ordered pair (8, -313) on the graph?

• It is a y-intercept.

• It is an x-intercept.

• It is a relative minimum.

• It is a relative maximum.

Between which x-values is the function decreasing?

• From 0 to 1.

• From negative infinity to 1.

• From 1 to 8.

• From 8 to infinity.

In interval notation, where is the function increasing?

• From 1 to infinity.

• From 0 to 1.

• From negative infinity to 1 and from 8 to infinity.

• From 1 to 8.

What is the purpose of plotting x-values on a number line?

• To identify intervals of increase and decrease.

• To find the exact value of y-intercepts.

• To determine the color of the graph.

• To change the graph type.