document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63101>Question 63101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a)determine whether the graph 0f 5x^2 -3y=4 is symmetric with respect to the y axis<BR>\n" );
document.write( "b)determine whether the function f(x)= x^4 +x^2+3 is even odd or neither<BR>\n" );
document.write( "c)Write an equation for a function that has a graph with the shape of y=square root of x but shifted to the right 7 units and up 4 units\r<BR>\n" );
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document.write( "thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #43923 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=43923\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)determine whether the graph 0f 5x^2 -3y=4 is symmetric with respect to the y axis<BR>\n" );
document.write( "If the function is even it's symmetric to the y-axis.  We know it's even if we substitute -x in for x and get the same function when you simplify.<BR>\n" );
document.write( "5(-x)^2-3y=4<BR>\n" );
document.write( "5(-x)(-x)-3y=4<BR>\n" );
document.write( "5x^2-3y=4<BR>\n" );
document.write( "It's even so it's symmetric to the y-axis.<BR>\n" );
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document.write( "b)determine whether the function f(x)= x^4 +x^2+3 is even odd or neither<BR>\n" );
document.write( "If f(-x)=f(x), it's even<BR>\n" );
document.write( "If f(-x)=-f(x), it's odd<BR>\n" );
document.write( "Otherwise it's neither.<BR>\n" );
document.write( "A quick way to check for polynomials is to see if all of the variables' exponents are even, because x^0=1, anything without an variable is even.  If this is true, it's even.<BR>\n" );
document.write( "If all of the variables have odd exponents, it's odd.<BR>\n" );
document.write( "If there's a mixture, it's neither.<BR>\n" );
document.write( "f(-x)=(-x)^4+(-x)^2+3<BR>\n" );
document.write( "f(-x)=x^4+x^2+3=f(x)  It's even.<BR>\n" );
document.write( ":\r<BR>\n" );
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document.write( "c)Write an equation for a function that has a graph with the shape of y=square root of x but shifted to the right 7 units and up 4 units<BR>\n" );
document.write( "horizontal shifts happen on the inside of the square root with a sign opposite to the direction of the shift.  <BR>\n" );
document.write( "Vertical shifts happen outside of the square root with a sign in the direction to the shift.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28x-7%29%2B4 ALIGN=MIDDLE  ALT=\"y=sqrt%28x-7%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Happy Calculating!!! </SPAN>\n" );
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