MATH 1314 Geogebra Commands Moving and Rescaling Click

MATH 1314 Geogebra Commands

Moving and Rescaling Click the cross-hairs icon. Using the mouse, click and drag to view other areas of the screen. Move over the x- or y-axis in order to rescale in the horizontal or vertical directions.

View or Options Menus In the downloaded version of the software, these menu options will appear at the top of the screen. In the online version of the software will have an icon with three horizontal bars on the upper right of the screen. Clicking this will give all the menu options.

Basic Commands Power: ^ (shift 6) Multiplication: * (shift 8) Division: / Square Root: sqrt() Cube Root: cbrt() Other Roots: Use fractional exponents

Inputting Functions: In the Input Box: f(x) = ……. g(x) = ……. Make sure you are using parenthesis when needed!! Evaluating a function at an x-value: f(x-value) g(x-value)

Roots (x-intercepts, zeros) Polynomial Functions: root[f(x)] Other Functions: root[g(x), left x, right x]

Relative Minimums and Relative Maximums These are the high points of the surrounds points or the low points of the surrounding points. Polynomial Functions: extremum[f(x)] Other Functions: extremum[g(x), left x, right x] You must visually determine if the coordinate point listed is a minimum or a maximum.

Points of Intersection: Polynomial Functions: Intersect[f(x), g(x)] Other Functions: Intersect[f(x), g(x), left x, right x]

Curves of Best Fit Under the View Menu: Select Spreadsheet. Input x-values in the first column, y-values in the second column Highlight all used cells Click the bottom arrow in the coordinate point button, select “List of Points”

Regression Curves: Polynomial: fitpoly[list 1, degree] Degree must be greater than or equal to 1: Linear: deg 1 Quadratic: deg 2 Cubic: deg 3 Others: Exponential: fitexp[list 1] Power Function: fitpow[list 1] Quartic: deg 4

Goodness of Fit To determine the r 2 value of a regression curve will tell you how good of a fit to the data it is. r 2 close to zero: poor fit to the data. r 2 close to one: good fit to the data. Regardless of the r 2 value, the curve must match the trend of the data to be a good predictor of long-term trends.

Limits: limit(function, x-value) For limits at infinity, type the word “infinity” or “-infinity” in place of the x-value. One sided limits: Limit. Above(function, x-value) will give the limit from the right. Limit. Below(function, x-value) will give the limit from the left.

Derivatives derivative(function) This will automatically define the derivative of f(x) as f’(x). You can find the numeric derivatives by inputting f’(x-value)

Tangent Lines: To find the equation of a tangent line to a function at a specific x-value: tangent[x-value, function]

Points of Inflection inflectionpoint(Polynomial) This will give the (x, y) coordinate of the point of inflection

Asymptotes asymptote[function] This command will give all vertical, horizontal and oblique asymptotes of the function (as x = p, y = q, or y = mx + b linear equations, respectively).

Rectangular Sums or Riemann’s Sums Rectangle. Sum(Function, Starting x, Stopping x, Number of Rectangles, Rectangle Position) Rectangle Position Options: 0 : Left corner touches graph 0. 5 : Midpoint touches graph 1 : Right corner touches graph This will return the area approximation between the curve and the xaxis between two x-values for a set number of rectangles.

Upper. Sum(Function, Starting x, Stopping x, Number of Rectangles) Lower. Sum(Function, Starting x, Stopping x, Number of Rectangles) These will return the overestimate or underestimate (regardless of rectangle position) for the area approximation using a fixed number of rectangles.

Integration: To calculate an Indefinite Integral: integral(function) Note: you must attach the constant of integration (+ C) at the end of the GGB output.

To calculate a Definite Integral: integral(function, starting x-value, ending x-value) This will return the numeric value for the area between the curve and the x-axis. This will be a signed (x/-) value.

Area Between Curves: To find the area between two graphs: Integral. Between(top-function, bottom-function, starting x-value, ending x-value) Note: You may need to use two separate commands if the top/bottom function switch partway through the problem. Second Note: You may need to find your start/stop values by using an intersect(polynomial 1, polynomial 2) or intersect(function 1, function 2, starting x, stopping x) command.