document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018514>Question 1018514</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	Consider the logarithmic equation f(x) = ln (x + 2) – 1. Round all values to the tenths place.<BR>\n" );
document.write( "(a)	Determine any x- and y-intercepts.<BR>\n" );
document.write( "(b)	Determine the domain and the equation of the vertical asymptote.<BR>\n" );
document.write( "(c)	Make a table of values to find three other points on the graph.<BR>\n" );
document.write( "(d)	Graph the function. Label the three points you found in Part (c).<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 #634597 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=634597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the graph of the equation of y = ln(x+2) - 1 is shown below.<BR>\n" );
document.write( "look below the graph for further comments.\r<BR>\n" );
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document.write( "your answers are described below.\r<BR>\n" );
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document.write( "Consider the logarithmic equation f(x) = ln (x + 2) – 1. Round all values to the tenths place.<BR>\n" );
document.write( "(a) Determine any x- and y-intercepts.\r<BR>\n" );
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document.write( "the x-intercept is found by setting y = 0 and solving for x.\r<BR>\n" );
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document.write( "y = ln(x+2)-1 becomes 0 = ln(x+2)-1.<BR>\n" );
document.write( "add 1 to both sides of this equation to get ln(x+2) = 1<BR>\n" );
document.write( "this is true if and only if e^1 = x+2<BR>\n" );
document.write( "solve for x to get x = .71828.....\r<BR>\n" );
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document.write( "the y-intercept is found by setting x = 0 and solving for y.<BR>\n" );
document.write( "y = ln(x+2)-1 becomes y = ln(2)-1.<BR>\n" );
document.write( "solve for y to get y = .30685...\r<BR>\n" );
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document.write( "these are rounded to 3 decimal places on the graph.\r<BR>\n" );
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document.write( "the vertical asymptote is found when the argument inside the equation of y = ln(x+2) - 1 is set to 0.\r<BR>\n" );
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document.write( "this occurs when x = -2 because -2 + 2 = 0.\r<BR>\n" );
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document.write( "any value of x less than or equal to -2 will be undefined.\r<BR>\n" );
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document.write( "any value of x greater than -2 will be defined.\r<BR>\n" );
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document.write( "as the value of x gets closer to 0 from the right, the value of y will get progressively larger in a negative direction.\r<BR>\n" );
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document.write( "so the value of y approaches negative infinity as x gets closer and closer to -2 from the right.\r<BR>\n" );
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document.write( "that's your vertical asymptote.\r<BR>\n" );
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document.write( "the function will get progressively larger as x becomes larger going in a positive direction.\r<BR>\n" );
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document.write( "there does not appear to be any limit to how high the value of y gets as far as i can see, although it does get up there very slowly.\r<BR>\n" );
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document.write( "for example, when x = 9 * 10^99, y = 229.15.\r<BR>\n" );
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document.write( "my calculator can't go higher than that, but it appears that there is no limit to the value of y, although the value of y increases extremely slowly in relation to x.\r<BR>\n" );
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document.write( "the value of y does not get closer and closer to a limit value, but just keeps getting higher and higher.\r<BR>\n" );
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document.write( "therefore, no horizontal asymptote as far as i can determine.\r<BR>\n" );
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document.write( "(b) Determine the domain and the equation of the vertical asymptote.\r<BR>\n" );
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document.write( "the domain is all real values of x > -2.<BR>\n" );
document.write( "the range is all real values of y.\r<BR>\n" );
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document.write( "(c) Make a table of values to find three other points on the graph.\r<BR>\n" );
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document.write( "this is easy enough for you to do.\r<BR>\n" );
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document.write( "simply choose some values of x and then solve the equation for y.\r<BR>\n" );
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document.write( "use your calculator to find three other values of x and then solve for y using your scientific calculator or an online scientific calculator if you don't have one.\r<BR>\n" );
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document.write( "the equation is y = ln(x+2) - 1\r<BR>\n" );
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document.write( "you already have the value of y when x = -2 (it's minus infinity), and when x = 0 (it's -.30685...).\r<BR>\n" );
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document.write( "(d) Graph the function. Label the three points you found in Part (c).\r<BR>\n" );
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document.write( "i did it for you.<BR>\n" );
document.write( "the three points i chose are shown in the following graph.<BR>\n" );
document.write( "using the desmos calculator, it's a simple matter of setting x equal to the values that you chose and then finding the intersection, which the desmos calculator will show you.<BR>\n" );
document.write( "the desmos calculator does round to 2 or 3 decimal places, so if you want better accuracy, then perform the calculations in your scientific calculator.<BR>\n" );
document.write( "here's the graph.\r<BR>\n" );
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