document.write( "Question 1179769: https://gyazo.com/6cca872e14f76df34ecefd2f460c3032 \n" ); document.write( "

Algebra.Com's Answer #809360 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
parent function: $\"+f%28x%29+=+sin%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Periodicity of sin (x ) is $\"+2pi+\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+sin%28x%29%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "This is the general equation for a sinusoidal function: \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+a+sin+%28k%28x-d%29%29+%2B+c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a\"$ determines amplitude:
\n" ); document.write( " $\"a+%3E+1\"$ or $\"+a+%3C+-1\"$ → vertical stretch
\n" ); document.write( " $\"-1+%3C+a+%3C+1\"$ → vertical compression
\n" ); document.write( " $\"a+%3C+0\"$ → reflection in $\"x\"$ -axis\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"k\"$ determines period:
\n" ); document.write( " $\"k+%3E1\"$ or $\"k+%3C+-1\"$ → horizontal compression by $\"1%2Fk\"$
\n" ); document.write( " $\"-1+%3C+k+%3C+1\"$ → horizontal stretch by $\"1%2Fk\"$
\n" ); document.write( " $\"k+%3C+0\"$ → reflection in $\"y\"$ -axis\r
\n" ); document.write( "\n" ); document.write( " $\"d\"$ determines phase shift:
\n" ); document.write( " $\"d+%3E+0\"$ → shift to the right \" $\"d\"$ \" units.
\n" ); document.write( " $\"d+=+0\"$ → no phase shift
\n" ); document.write( " $\"d+%3C+0\"$ → shift to the left \" $\"d\"$ \" units\r
\n" ); document.write( "\n" ); document.write( " $\"c\"$ determines vertical shift:
\n" ); document.write( " $\"c+%3E+0\"$ → shift up \"c\" units
\n" ); document.write( " $\"c+=+0\"$ → no vertical shift
\n" ); document.write( " $\"c+%3C+0\"$ → shift down \" $\"c\"$ \" units\r
\n" ); document.write( "\n" ); document.write( "you are given:\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+3sin+%282%28x-pi%2F6%29%29+%2B+1\"$ \r
\n" ); document.write( "\n" ); document.write( "so, in this case \r
\n" ); document.write( "\n" ); document.write( "periodicity is $\"+2pi%2Fk=2pi%2F2=pi+\"$
\n" ); document.write( " $\"a=3\"$ => $\"+a+%3E+1+\"$ → vertical stretch
\n" ); document.write( " $\"k=2\"$ => $\"k+%3E1\"$ → horizontal compression by $\"1%2Fk=1%2F2\"$
\n" ); document.write( " $\"d=pi%2F6\"$ => $\"d+%3E+0\"$ → shift to the right \" $\"pi%2F6\"$ \" units
\n" ); document.write( " $\"c=1\"$ => $\"c+%3E+0\"$ → shift up \" $\"1\"$ \" unit\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );