Round to the nearest thousandth.Solve [latex]5\mathrm{log}\left(x+2\right)=4-\mathrm{log}\left(x\right)[/latex] graphically. State the domain, range, and asymptote.The domain is [latex]\left(0,\infty \right)[/latex], the range is [latex]\left(-\infty ,\infty \right)[/latex], and the vertical asymptote is

Log In Function Transformations: Horizontal and Vertical Stretch and Compression This video explains to graph graph horizontal and vertical stretches and compressions in the form af(b(x-c))+d. Substituting [latex]\left(-1,1\right)[/latex],[latex]\begin{array}{llll}1=-a\mathrm{log}\left(-1+2\right)+k\hfill & \text{Substitute }\left(-1,1\right).\hfill \\ 1=-a\mathrm{log}\left(1\right)+k\hfill & \text{Arithmetic}.\hfill \\ 1=k\hfill & \text{log(1)}=0.\hfill \end{array}[/latex]Next, substituting [latex]\left(2,-1\right)[/latex],[latex]\begin{array}{llllll}-1=-a\mathrm{log}\left(2+2\right)+1\hfill & \hfill & \text{Plug in }\left(2,-1\right).\hfill \\ -2=-a\mathrm{log}\left(4\right)\hfill & \hfill & \text{Arithmetic}.\hfill \\ \text{ }a=\frac{2}{\mathrm{log}\left(4\right)}\hfill & \hfill & \text{Solve for }a.\hfill \end{array}[/latex]This gives us the equation [latex]f\left(x\right)=-\frac{2}{\mathrm{log}\left(4\right)}\mathrm{log}\left(x+2\right)+1[/latex].We can verify this answer by comparing the function values in the table below with the points on the graph in this example.Give the equation of the natural logarithm graphed below.f\left(x\right)=2\mathrm{ln}\left(x+3\right)-1[/latex]

The lesson Graphing Tools: Vertical and Horizontal Scaling in the Algebra II curriculum gives a thorough discussion of horizontal and vertical stretching and shrinking. The kinds of changes that we will be making to our logarithmic functions are horizontal and vertical stretching and compression. State the domain, range, and asymptote.The domain is [latex]\left(2,\infty \right)[/latex], the range is [latex]\left(-\infty ,\infty \right)[/latex], and the vertical asymptote is When the parent function [latex]f\left(x\right)={\mathrm{log}}_{b}\left(x\right)[/latex] is multiplied by –1, the result is a The function [latex]f\left(x\right)={\mathrm{-log}}_{b}\left(x\right)[/latex]The function [latex]f\left(x\right)={\mathrm{log}}_{b}\left(-x\right)[/latex]The graphs below summarize the key characteristics of reflecting [latex]f(x) = \log_{b}{x}[/latex] horizontally and vertically.Sketch a graph of [latex]f\left(x\right)=\mathrm{log}\left(-x\right)[/latex] alongside its parent function. State the domain, range, and asymptote.Before graphing [latex]f\left(x\right)=\mathrm{log}\left(-x\right)[/latex], identify the behavior and key points for the graph.The domain is [latex]\left(-\infty ,0\right)[/latex], the range is [latex]\left(-\infty ,\infty \right)[/latex], and the vertical asymptote is x = 0.Graph [latex]f\left(x\right)=-\mathrm{log}\left(-x\right)[/latex]. The graph approaches x = –3 (or thereabouts) more and more closely, so x = –3 is, or is very close to, the vertical asymptote. It looks at how a and b affect the graph of f(x). State the domain, range, and asymptote.Remember, what happens inside parentheses happens first. Examples of Horizontal Stretches and Shrinks . Include the key points and asymptotes on the graph. Include the key points and asymptote on the graph. We can shift, stretch, compress, and reflect the The graphs below summarize the changes in the x-intercepts, vertical asymptotes, and equations of a logarithmic function that has been shifted either right or left.Sketch the horizontal shift [latex]f\left(x\right)={\mathrm{log}}_{3}\left(x - 2\right)[/latex] alongside its parent function. Round to the nearest thousandth.Now that we have worked with each type of transformation for the logarithmic function, we can summarize each in the table below to arrive at the general equation for transforming exponential functions.All transformations of the parent logarithmic function [latex]y={\mathrm{log}}_{b}\left(x\right)[/latex] have the form[latex] f\left(x\right)=a{\mathrm{log}}_{b}\left(x+c\right)+d[/latex]where the parent function, [latex]y={\mathrm{log}}_{b}\left(x\right),b>1[/latex], isFor [latex]f\left(x\right)=\mathrm{log}\left(-x\right)[/latex], the graph of the parent function is reflected about the What is the vertical asymptote of [latex]f\left(x\right)=-2{\mathrm{log}}_{3}\left(x+4\right)+5[/latex]?The coefficient, the base, and the upward translation do not affect the asymptote. The shift of the curve 4 units to the left shifts the vertical asymptote to What is the vertical asymptote of [latex]f\left(x\right)=3+\mathrm{ln}\left(x - 1\right)[/latex]?Find a possible equation for the common logarithmic function graphed below. Include the key points and asymptote on the graph. For example, look at the graph in the previous example. You make horizontal changes by adding a […]

The graphical representation of function (1), f (x), is a parabola.. What do you suppose the grap Include the key points and asymptote on the graph. We can shift, stretch, compress, and reflect the parent function y = logb(x) without loss of shape.