Technology Can Be Deceiving…

Suppose you are asked to determine whether a function is discontinuous. Many of you might use technology to help you graph a function to decide what the limits are from the left and right. Remember, a function is continuous at a point if the limits from the left and right are equal and also match the value of the function at the point.

Be aware that the TI calculators, WolframAlpha, and Desmos may give slightly different graphs and lead you to the wrong conclusion.

The new MathFAQ below demonstrates how to graph

in WolframAlpha and Desmos.

Notice how the graphs differ. Which one is the better graph to use if you are deciding if the function is discontinuous?

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What is the Difference Between A Secant Line and a Tangent Line?

 

Many students struggle with slopes of tangent lines versus slopes of secant lines. In the example below, I find these slopes and use them to compute the equation of a tangent line and the equation of a secant line.

The secant line is the red line to the right that passes through two points on the curve. The tangent line is the green line that just grazes the curve at a point.

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