SOLUTION: Sketch two periods of the graph for the following function. f(x) = 5 sec(3x) Identify the stretching factor and period. Identify the asymptotes in the displayed domain of the gr

Algebra ->  Trigonometry-basics -> SOLUTION: Sketch two periods of the graph for the following function. f(x) = 5 sec(3x) Identify the stretching factor and period. Identify the asymptotes in the displayed domain of the gr      Log On


   

Question 1203780: Sketch two periods of the graph for the following function.
f(x) = 5 sec(3x)
Identify the stretching factor and period.
Identify the asymptotes in the displayed domain of the graph you selected above. (Enter your answers as a comma-separated list of equations.)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+5sec%283x%29
stretching factor: Stretched vertically by 5
period: %282pi%29%2F3
Vertical asymptotes
x=pi%2F2%2B%282pi%2F3%29n
x=pi%2F6%2B%282pi%2F3%29n where n is an integer
in two period distance are
1%2F4 and 3%2F4+of the distance between+0 and %282pi%29%2F3, and the distance between 0+and -%282pi%29%2F3
x=%281%2F4%29%280%2B%282pi%29%2F3%29=pi%2F6
x=%283%2F4%29%280%2B%282pi%29%2F3%29=3pi%2F6=pi%2F2
similarly
x=-pi%2F6
x=-pi%2F2
download-1


Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
Sketch two periods of the graph for the following function.
f(x) = 5 sec(3x)
Identify the stretching factor and period.
Identify the asymptotes in the displayed domain of the graph you selected above.
(Enter your answers as a comma-separated list of equations.)
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        Teaching by  @MathLover1 in her post is  INCORRECT  and  WRONG.

        Many of her numbers are wrong; her argumentation is defective; her explanations are incorrect.

        I came to bring correct answers to posed questions and to make this job in a way as it should be done. 


(1)  To sketch the plot, go to web-site www.desmos.com/calculator

     Find there free of charge plotting tool for common use.

     Print the equation of the function and get the plot in the next instance.



(2)  In this problem, there are 2 (two) stretching factors: one vertical and one horizontal, 
     and both deserves to be discussed.

     Vertical stretching factor is 5.  It is the coefficient (multiplier) before the function "sec".

     In this problem, this coefficient is greater than 1, so it really produces vertical stretching 
     with coefficient 5.


     Horizontal stretching coefficient is 1/3, and because it is less than 1, in this problem 
     it is better to speak about horizontal compression with coefficient 3.

     The period is  2pi%2F3.


(3)  Since  5sec(3x) = 5%2Fcos%283x%29, vertical asymptotes are where cos(3x) is zero.

     cos(3x) is zero where 3x = pi%2F2+%2B+k%2Api,  or  at  x= pi%2F6+%2B+k%2A%28pi%2F3%29,  k= 0, +/-1, +/-2, . . . 

     So, vertical asymptotes are at x= pi%2F6+%2B+k%2A%28pi%2F3%29,  k= 0, +/-1, +/-2, . . . 

     First two vertical asymptotes in positive domain are at x= p%2F6+%2B+pi%2F3  and  x= pi%2F6+%2B+%282pi%29%2F3.

Solved and answered in correct form,  as it should be done,
with explanations where necessary.