Everything Maths Grade 10

Discovering the characteristics EMA5H

Domain and range

From the graph we see thattanis undefined at= 90°and= 270°.

Therefore the domain isf: 0° 360 °; ̸= 90°; 270°g.

The range isff() :f() 2 Rg.

Period

The period ofy=atan+qis 180 °. This means that one tangent cycle is completed in 180 °.

Intercepts

They-intercept off() =atan+qis simply the value off()at= 0°.

y=f(0°)

=atan 0 °+q

=a(0) +q

=q

This gives the point(0°;q).

Asymptotes

The graph has asymptotes at= 90°and= 270°.

Worked example 21: Sketching a tangent graph

QUESTION

Sketch the graph ofy= 2tan+ 1for 2 [0°; 360°].

SOLUTION

Step 1: Examine the standard form of the equation

We see thata > 1 so the branches of the curve will be steeper. We also see thatq > 0 so the graph is shifted

vertically upwards by 1 unit.

Step 2: Substitute values for

 0 ° 30 ° 60 ° 90 ° 120 ° 150 ° 180 ° 210 ° 240 ° 270 ° 300 ° 330 ° 360 °

y 1 2,15 4,46 – 2,46 0,15 1 2,15 4,46 – 2,46 0,15 1

Chapter 6. Functions 199