Worksheet 2: Graphs, Functions and Derivatives

Put everything together in a picture. Scholars take what they learned in the previous three lessons in the 15th segment of a 23-part unit to graph rational functions. They find the end behavior, the horizontal and vertical asymptotes if...

The slider feature on Desmos excellently shows how graphs change based on different variable values. Learners look at two similar rational functions and compare and discuss what happens when the numbers go from positive to zero to...

Double win with a comprehensive worksheet and an excellent worked out answer key. The worksheet itself is twelve pages and begins with the simple sine and cosine graphs, then, develops into the reciprocal trig functions. 

Move all rational functions—well, maybe. Learners investigate the graphs of the reciprocals of power functions to determine a pattern between the graph and the power. Pupils graph rational functions where transformations are clearly...

Sometimes graphing rational functions can feel a little "irrational." Starting with the basics, learners work their way through the pieces of these graphs and finish off with an application question. 

Find deeper meaning in graphs. Pupils use the knowledge gained from the previous sections in the unit to sketch graphs of a function's derivative. Learners also see how to sketch a graph of a function given the graph of its derivatives....

Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...

Shift the function and transform the key features of the graph. By translating the graph of the rational function, class members find out how the key features alter. Pupils determine the domain, range, asymptotes, and intervals of...

Section 9 of the 12 linked Saxon Math sections introduces the young algebrist to graphing periodic functions, creating graphs from quadratic roots, working with inequalities, and rational equations. Common among all the lessons is the...

So, exactly, what does it look like? The easily usable graphing calculator allows pupils to visualize the graph of equations and inequalities. The interactive supports any algebraic graph needed for high school mathematics and then some.