How can i graph this functions and include two full period?

Question

Graph the functions and include two full period.

 

1) y=-3 tan πx

 

2) y=2 sec 4x

 

3) y= csc x/3

 

4) y= 3 cot πx/2

 

     If i dont have a graphing calculator and i need to show my graph can i use GeoGebra to copy that Graph?

Answer 1

Graph the functions and include two full periods.

 

I've changed the symbol for pi to pi because the symbol doesn't resolve well (looks like the symbol for en in my browser). Also, it's much better to use functional notation and enclose all function arguments in parentheses.

1) y = -3 tan πx = -3 tan(pi x)

 

The period length of tangent is pi, so if you pick 0 as the start of your graph, then your graph's domain would be:

 

0 ≤ (pi x) < (2 pi), or 0 ≤ x < 2. (Divided by pi.)

 

Here's a GeoGebra graph: http://www.wyzant.com/resources/files/267101/2_periods_of_a_tangent_function

2) y = 2 sec 4x = 2 sec(4x)

 

Secant is 1/cosine so they both have a period length of 2 pi. We want 2 periods so we could use:

 

0 ≤ (4x) < 2(2 pi) or 0 ≤ x < pi

 

Here's a GeoGebra graph: http://www.wyzant.com/resources/files/267103/2_periods_of_a_secant_function

3) y = csc x/3 = csc(x/3)

4) y = 3 cot πx/2 = 3 cot(x pi/2)

If I don't have a graphing calculator and I need to show my graph can I use GeoGebra to copy that Graph graph it?

 

If you were in my class, I would say YES! Your teacher should be happy you are learning to use technology for math; and if you can use a graphing calculator, you should be able to use GeoGebra. But DO ask your teacher.