document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=108601>Question 108601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I answer these problems I am really stuck.  Any help would be greatly appreciated.  Thank you.\r<BR>\n" );
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document.write( "Suppose the graph of y = x^2  is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?\r<BR>\n" );
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document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%09Combining+Horizontal+and+Vertical+Shifts+ ALIGN=MIDDLE  ALT=\"+graph%09Combining+Horizontal+and+Vertical+Shifts+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Cannot copy and paste this graph)for this parablola<BR>\n" );
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document.write( "Answer: g(x) = (x + 1)^2 – 3 (vertical shift down 3 units) Y = X^2 - 3<BR>\n" );
document.write( "	Is this right???								\r<BR>\n" );
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document.write( "b)	<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph+ ALIGN=MIDDLE  ALT=\"+graph+\"   DISABLED_style= \"max-width:90%; height:auto;\" > x , y, axis U shape goes right over 4 on the x axis<BR>\n" );
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document.write( "Answer: g(x) = (x – 4)^2 (horizontal shift right 4 units) Is this right???\r<BR>\n" );
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document.write( "3)	Consider the following graph of y = f(x).  \r<BR>\n" );
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document.write( "a)	If h(x) = f(x) + 2, what would the new coordinates of P be after the shift?  Give answer in (x, y) form.\r<BR>\n" );
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document.write( "	Answer:\r<BR>\n" );
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document.write( "b)	If  , what would the new coordinates of P be after the reflection?  Give answer in (x, y) form.\r<BR>\n" );
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document.write( "	Answer:\r<BR>\n" );
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document.write( "4)	Consider the function: f(x)= x^2+ 4x + 1 \r<BR>\n" );
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document.write( "a)	Find h, the x-coordinate of the vertex of this parabola.<BR>\n" );
document.write( "	Answer:<BR>\n" );
document.write( "	Show your work here:\r<BR>\n" );
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document.write( "b)	Substitute the two whole number values immediately to the left and right of h into the function to find the corresponding y.  Fill in the following table. Make sure your x-values are in increasing order in your table.\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "x	y<BR>\n" );
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document.write( "h =__	<BR>\n" );
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document.write( "c)	Use MS Excel to graph the function by plotting the points found in the table in part b.  \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "5)	Find the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote.\r<BR>\n" );
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document.write( "a)f(x)= 2x+3/x+2	 		\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "Horizontal:<BR>\n" );
document.write( "Vertical:\r<BR>\n" );
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document.write( "b)g(x)= 5x/x^2+1	 \r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "Horizontal:<BR>\n" );
document.write( "Vertical:\r<BR>\n" );
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document.write( "c)	\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "Horizontal:<BR>\n" );
document.write( "Vertical:\r<BR>\n" );
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document.write( "d)\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "Horizontal:<BR>\n" );
document.write( "Vertical:\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79179 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=79179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How would I answer these problems I am really stuck. Any help would be greatly appreciated. Thank you. <BR>\n" );
document.write( "Suppose the graph of y = x^2 is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph? <BR>\n" );
document.write( "a)g(x) = (x + 1)^2 – 3<BR>\n" );
document.write( "The (x+1) moves each point of y=x^2 one to the left<BR>\n" );
document.write( "The -3 moves the result of the 1st move down three.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=How+would+I+answer+these+problems+I+am+really+stuck.+Any+help+would+be+greatly+appreciated.+Thank+you.+%0D%0ASuppose+the+graph+of+y+=+x%5E2+is+shifted+to+obtain+each+the+following+graphs.+What+is+the+equation+of+the+function%2C+g%28x%29%2C+for+each+graph%3F+%0D%0Aa%29g%28x%29+=+%28x+%2B+1%29%5E2+%96+3%0D%0AThe+%28x%2B1%29+moves+each+point+of+y=x%5E2+one+to+the+left%0D%0AThe+-3+moves+the+result+of+the+1st+move+down+three.%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >graph(400,300,-10,10,-10,10,(x+1)^2-3<BR>\n" );
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document.write( "Answer: b)  x , y, axis U shape goes right over 4 on the x axis\r<BR>\n" );
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document.write( "Answer: g(x) = (x – 4)^2 (horizontal shift right 4 units) Is this right??? <BR>\n" );
document.write( "Yes, that is correct.<BR>\n" );
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document.write( "3) Consider the following graph of y = f(x). \r<BR>\n" );
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document.write( "a) If h(x) = f(x) + 2, what would the new coordinates of P be after the shift? Give answer in (x, y) form. <BR>\n" );
document.write( "Answer: (x, f(x)+2)<BR>\n" );
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document.write( "b) If , what would the new coordinates of P be after the reflection? Give answer in (x, y) form. <BR>\n" );
document.write( "Answer: That depends on what line you reflect in:<BR>\n" );
document.write( "If you reflect in the y-axis the answer is (-x,h(x))<BR>\n" );
document.write( "If you reflect in the x-axis the anser is (x,-h(x))<BR>\n" );
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document.write( "4) Consider the function: f(x)= x^2+ 4x + 1 <BR>\n" );
document.write( "a) Find h, the x-coordinate of the vertex of this parabola.<BR>\n" );
document.write( "Answer: (-2,-3)<BR>\n" );
document.write( "Show your work here:<BR>\n" );
document.write( "Complete the square on the x-terms:<BR>\n" );
document.write( "x^2+4x +? = f(x)-1+?<BR>\n" );
document.write( "x^2+4x+4 = f(x)+3<BR>\n" );
document.write( "(x+2)^2 = f(x)+3<BR>\n" );
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document.write( "b) Substitute the two whole number values immediately to the left and right of h into the function to find the corresponding y. Fill in the following table. Make sure your x-values are in increasing order in your table. <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "f(x)= x^2+ 4x + 1 <BR>\n" );
document.write( "x y<BR>\n" );
document.write( "If x = -4, y = 16-16+1 = 1<BR>\n" );
document.write( "If x = -3, y = 9-12+1 = -2<BR>\n" );
document.write( "If x = -1, y = 1-4+1 = -2<BR>\n" );
document.write( "If x = 0, y = 0+0+1 = 1\r<BR>\n" );
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document.write( "h =__ \r<BR>\n" );
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document.write( "c) Use MS Excel to graph the function by plotting the points found in the table in part b. <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
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document.write( "5) Find the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote. <BR>\n" );
document.write( "a)f(x)= 2x+3/x+2 <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "Horizontal:y = 2x/x = 2<BR>\n" );
document.write( "Vertical: x = -2<BR>\n" );
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document.write( "b)g(x)= 5x/x^2+1 <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "Horizontal: y = 0x^2/x^2 = 0<BR>\n" );
document.write( "Vertical: none since x^2+1 cannot be zero<BR>\n" );
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document.write( "c) \r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "Horizontal:<BR>\n" );
document.write( "Vertical: <BR>\n" );
document.write( "d) \r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "Horizontal:<BR>\n" );
document.write( "Vertical: <BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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