Graphing functions

8.1Enter a function in the Y= editor#

Graphing starts in the Y= editor. It has ten function slots, Y1 to Y9 and Y0. Each slot holds a rule in terms of x. Type the rule, using X,T,θ,n for x, and press ▼ or enter to go to the next slot. The black square before a name means the slot is switched on.

Example 8.1

Graph y = x² − 4

$$y=x^{2}-4$$

1. Press Y= and type X, the square key, minus, 4. Use the X,T,θ,n key for X.

   y=X,T,θ,nx²−4

   

2. Press graph to draw it. The cursor then keeps the same view; press trace to read points.

   graphtrace

Example 8.2

Several functions at once

1. Type X in Y1 and −X in Y2, then press the down key to leave Y2 and graph.

   y=X,T,θ,n▼(−)X,T,θ,n▼trace

Press clear in a slot to erase its rule, or del to delete single characters. Menu items such as abs( from math can be pasted into Y=.

Example 8.3

Paste a function from a menu

1. In Y= press math, right (NUM), 1 for abs(, then X and a bracket.

   y=math▶1X,T,θ,n)

8.2Turn a function on or off#

Only functions that are on (black square) are drawn. To switch one off, move the cursor left onto the equals sign and press enter. Press enter again to switch it back on. Switching off keeps the rule, so you can compare graphs without retyping.

Example 8.4

Switch Y1 off

1. Type X in Y1, move left twice onto the equals sign and press enter. The black square disappears.

   y=X,T,θ,n◀◀enter

The row at the top of the editor, Plot1 Plot2 Plot3, switches statistics plots on and off the same way (move ▲ onto it and press enter).

Example 8.5

Switch Plot1 on

1. In Y= press up onto the Plot row, then enter.

   y=▲enter

8.3Change the colour of a graph#

Each slot has a colour. The defaults are blue, red, black, magenta, green and so on. Move the cursor left past the equals sign onto the colour marker and press enter to step to the next colour.

Example 8.6

Make Y1 red

1. Type X in Y1, move left three times and press enter.

   y=X,T,θ,n◀◀◀enter

8.4Use a Y= function on the home screen#

A function stored in Y1 can be used like any function: Y1(2) evaluates it at 2. Paste the name from vars, then ▶ (Y-VARS), then 1 (Function) and the slot number.

Example 8.7

Evaluate Y1(2)

$$y=x^2+1,\quad y(2)=5$$

1. Store X²+1 in Y1.

   y=X,T,θ,nx²+1

2. Go home, paste Y1 through vars, right, 1, 1 and type (2).

   2ndQUITmodevars▶11(2)enter

Example 8.8

Store text into Y1

1. Type "2X" with the quote key (alpha add), press sto and paste Y1 with vars, right, 1, 1, then enter. Open Y= to see it.

   alpha"+2X,T,θ,nalpha"+sto→vars▶11entery=

8.5Graph parametric equations#

In parametric mode a point moves with a parameter t: $x=f(t)$ and $y=g(t)$. Set MODE to PAR (fourth row). The Y= editor then shows pairs X1T and Y1T, the WINDOW screen asks for Tmin, Tmax and Tstep, and X,T,θ,n types T.

Example 8.9

Graph a circle

1. Choose PAR in MODE.

   mode▼▼▼▶enter

2. In Y= type cos(T) for X1T, press down, type sin(T) for Y1T.

   y=cosX,T,θ,n)▼sinX,T,θ,n)

   

3. Press graph, then trace. The screen shows the value of T and the point.

   graphtrace

Example 8.10

The WINDOW screen in parametric mode

1. In PAR mode press window.

   mode▼▼▼▶enterwindow

8.6Graph polar equations#

In polar mode you give the distance $r$ from the centre as a function of the angle $\theta$. Choose POL in MODE. Y= shows r1 to r6, WINDOW asks for θmin, θmax and θstep, and X,T,θ,n types θ.

Example 8.11

Graph a rose

1. Choose POL in MODE.

   mode▼▼▼▶▶enter

2. In Y= type 2 sin(3θ), using the X,T,θ,n key for θ.

   y=2sin3X,T,θ,n)

   

3. Press graph and then trace.

   graphtrace

8.7Grid, axes, labels and coordinates (FORMAT)#

Press 2ndFORMATzoom for FORMAT. Each row has two choices, with the current one in brackets. Choose with ◀ and ▶ and press enter.

Example 8.12

Turn the grid on

1. Open FORMAT, move down two rows, right to GridOn and enter.

   2ndFORMATzoom▼▼▶enter