document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164583>Question 1164583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> F(x)= {x^2 for <(with line underneath< )-3<BR>\n" );
document.write( "           9-x^2 for -3< x < ( with line underneath<) 3<BR>\n" );
document.write( "            X^2 for x>3\r<BR>\n" );
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document.write( "Find f(-3)\r<BR>\n" );
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document.write( "Find f(3)<BR>\n" );
document.write( "                        </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854344 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2264)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the values of the piecewise function $F(x)$ at specific points, we must identify which interval the given $x$-value falls into and use the corresponding formula.\r<BR>\n" );
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document.write( "The function is defined as:<BR>\n" );
document.write( "$$F(x) = <BR>\n" );
document.write( "\begin{cases} <BR>\n" );
document.write( "x^2 & \text{if } x \le -3 \\<BR>\n" );
document.write( "9 - x^2 & \text{if } -3 < x \le 3 \\<BR>\n" );
document.write( "x^2 & \text{if } x > 3 <BR>\n" );
document.write( "\end{cases}$$\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### **1. Find $f(-3)$**<BR>\n" );
document.write( "* **Identify the interval:** We look for the condition that includes $-3$. The first part of the function is defined for $x \le -3$ (\"less than or equal to\").<BR>\n" );
document.write( "* **Apply the formula:** $F(x) = x^2$<BR>\n" );
document.write( "* **Calculation:** $$F(-3) = (-3)^2 = 9$$\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### **2. Find $f(3)$**<BR>\n" );
document.write( "* **Identify the interval:** We look for the condition that includes $3$. The middle part of the function is defined for $-3 < x \le 3$ (\"greater than $-3$ and less than or equal to $3$\").<BR>\n" );
document.write( "* **Apply the formula:** $F(x) = 9 - x^2$<BR>\n" );
document.write( "* **Calculation:** $$F(3) = 9 - (3)^2$$<BR>\n" );
document.write( "    $$F(3) = 9 - 9 = 0$$\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### **Summary of Results**<BR>\n" );
document.write( "* **$f(-3) = 9$**<BR>\n" );
document.write( "* **$f(3) = 0$** </SPAN>\n" );
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