Graph

Plot and examine functions.

Entering functions

1. Tap the Function Definer button (f(x)). Ten rows f₁(x) to f₁₀(x) appear.
2. Enter the functions as they appear in the textbook: with fractions, brackets and powers. Enter moves to the next row.
3. Tap Done or Draw.

• The tick in front of a row shows or hides the function.
• The colour square at the end of the row changes colour, line style and width.
• A function from Analysis, such as g(x), can be used here directly.
• If a row contains a y, CASDesk draws it as an equation, for example a circle x² + y² = 25.
• Parameters: any other letter without a value becomes a slider, for example a and b in a·sin(b·x). Tapping the slider's name sets its range. Moving it recalculates the curve and its analyses at once.

View

• ±5 range, ±10, ±100, ±1000 set the x-axis to that range; the y-axis follows.
• Axis Ranges sets x min, x max, y min and y max; expressions such as π are allowed. Tick Distances sets the axis scale.
• Box zoom: tap the button, then drag a rectangle around the part you want to see. Grid Settings shows a grid and sets it up.
• Zoom in and Zoom out zoom about the centre. The mouse wheel or two fingers zoom at a particular spot; dragging moves the picture.
• Tapping an axis arrowhead holds that axis while zooming and moving. A second tap releases it.

Examining functions

The mode buttons on the left examine the functions drawn:

• Which function? If you tap a curve first, it is selected and examined at once. Otherwise CASDesk asks which function you mean.
• Visible range: the search covers the part currently on screen. To find more, move the picture and tap the button again.
• Results appear as crosses on the curve. The selected point shows its coordinates, such as (2 | −2), with dashed lines to the axes. The arrow keys ← → step from point to point.
• Exact or decimal: with Fraction, CASDesk shows coordinates exactly where it can, for example √2.
• Removing: tapping the selected point again removes that whole analysis. Edit → Clear All removes all analyses; the functions stay.

Definite integral

1. Tap Definite Integral.
2. Enter the bounds a and b. If you have found zeros or intersections first, tapping their crosses fills the bounds one after the other.
3. Confirm with OK. The area is shaded in the function's colour, and the value appears at the top left, for example ∫ = 32/3.

• area between gives the area between two functions.
• |∫| counts areas below the x-axis as positive.
• + additional integral adds up to six sections, for example from zero to zero.
• Tapping a shaded area removes that integral.

Table of values

The Table button shows a table of values for all visible functions. Set x start, x end and step and tap Compute. Draw goes back to the graph.

Measured data and regression

1. Data Entry: enter the x and y values in the two rows; the table grows by itself. OK shows the points on the graph. Points from the spreadsheet come over with Plot in Graph mode (see Spreadsheet).
2. Regression Fit: choose the data series and the type, for example linear, quadratic, exponential, power, logarithmic, sinusoidal or logistic, and tap Compute Fit. You get the equation and the coefficient of determination R².
3. Store keeps the fitted function under a name and draws it as a function.

Taking the graph to the notebook

Edit → Diagram to the notebook puts the graph, with all its points and areas, into the notebook as a card. The same menu exports or copies it as an image.