Graphing Functions and Derivatives

The video tutorial introduces students to using Desmos for graphing functions and exploring derivatives. It begins with setting up function notation and progresses to exploring various functions and their derivatives. The tutorial emphasizes checking and comparing derivatives with expected results, analyzing hyperbolas, and understanding how differentiation affects the power of functions. The session is interactive, encouraging students to experiment with different functions and observe the outcomes.

What tool does the teacher ask students to use for graphing functions?

• GeoGebra

• Wolfram Alpha

• Desmos

• GraphCalc

What notation is used to represent a function in Desmos?

• k(x)

• f(x)

• h(x)

• g(x)

What is the purpose of the differential operator in Desmos?

• To plot points

• To integrate functions

• To find the derivative of functions

• To solve equations

Which button in Desmos is used to find the derivative of a function?

• Σ

• √

• d/dx

• ∫ dx

What is the derivative of a cubic function generally called?

• Cubic

• Linear

• Quadratic

• Quartic

What should you do if the derivative graph does not match your expectations?

• Change the function

• Ignore the discrepancy

• Use a different tool

• Recheck your algebra

What shape is the original graph when the function is x - 1 on x + 1?

• Parabola

• Ellipse

• Circle

• Hyperbola

What is an increasing function?

• A function that oscillates

• A function that always increases

• A function that remains constant

• A function that always decreases

What happens to the power of a polynomial function when it is differentiated?

• It doubles

• It remains the same

• It increases by one

• It decreases by one

What is the result of differentiating a function in terms of its graph?

• It shows the maximum value

• It finds the roots of the function

• It provides the slope of the tangent

• It gives the area under the curve