document.write( "Question 1203780: Sketch two periods of the graph for the following function.
\n" ); document.write( "f(x) = 5 sec(3x)
\n" ); document.write( "Identify the stretching factor and period.
\n" ); document.write( "Identify the asymptotes in the displayed domain of the graph you selected above. (Enter your answers as a comma-separated list of equations.) \n" ); document.write( "

Algebra.Com's Answer #839636 by ikleyn(52858) $\"\"$ $\"About$

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\n" ); document.write( "Sketch two periods of the graph for the following function.
\n" ); document.write( "f(x) = 5 sec(3x)
\n" ); document.write( "Identify the stretching factor and period.
\n" ); document.write( "Identify the asymptotes in the displayed domain of the graph you selected above.
\n" ); document.write( "(Enter your answers as a comma-separated list of equations.)
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\n" ); document.write( "\n" ); document.write( "        Teaching by @MathLover1 in her post is INCORRECT and WRONG.\r
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\n" ); document.write( "\n" ); document.write( "        Many of her numbers are wrong; her argumentation is defective; her explanations are incorrect.\r
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\n" ); document.write( "\n" ); document.write( "        I came to bring correct answers to posed questions and to make this job in a way as it should be done.\r
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document.write( "(1)  To sketch the plot, go to web-site www.desmos.com/calculator\r\n" );
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document.write( "     Find there free of charge plotting tool for common use.\r\n" );
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document.write( "     Print the equation of the function and get the plot in the next instance.\r\n" );
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document.write( "(2)  In this problem, there are 2 (two) stretching factors: one vertical and one horizontal, \r\n" );
document.write( "     and both deserves to be discussed.\r\n" );
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document.write( "     Vertical stretching factor is 5.  It is the coefficient (multiplier) before the function \"sec\".\r\n" );
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document.write( "     In this problem, this coefficient is greater than 1, so it really produces vertical stretching \r\n" );
document.write( "     with coefficient 5.\r\n" );
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document.write( "     Horizontal stretching coefficient is 1/3, and because it is less than 1, in this problem \r\n" );
document.write( "     it is better to speak about horizontal compression with coefficient 3.\r\n" );
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document.write( "     The period is  .\r\n" );
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document.write( "(3)  Since  5sec(3x) = , vertical asymptotes are where cos(3x) is zero.\r\n" );
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document.write( "     cos(3x) is zero where 3x = ,  or  at  x= ,  k= 0, +/-1, +/-2, . . . \r\n" );
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document.write( "     So, vertical asymptotes are at x= ,  k= 0, +/-1, +/-2, . . . \r\n" );
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document.write( "     First two vertical asymptotes in positive domain are at x=   and  x= .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and answered in correct form, as it should be done,
\n" ); document.write( "with explanations where necessary.\r
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