The vertical asymptote will be shifted to The domain is [latex]\left(-2,\infty \right)[/latex], the range is [latex]\left(-\infty ,\infty \right)[/latex], and the vertical asymptote is x = –2.Sketch a graph of the function [latex]f\left(x\right)=3\mathrm{log}\left(x - 2\right)+1[/latex]. Which of the following functions represents the transformed function (blue line… Examples of Horizontal Stretches and Shrinks . Learn how to do this with our example questions and try out our practice problems.

Vertical/Horizontal Stretching/Shrinking usually changes the shape of a graph. State the domain, range, and asymptote.Remember, what happens inside parentheses happens first. Include the key points and asymptote on the graph. Show Step-by-step Solutions 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. 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. It looks at how a and b affect the graph of f(x). 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.Since the function is [latex]f\left(x\right)=2{\mathrm{log}}_{4}\left(x\right)[/latex], we will note thatThis means we will stretch the function [latex]f\left(x\right)={\mathrm{log}}_{4}\left(x\right)[/latex] by a factor of 2.Consider the three key points from the parent function, [latex]\left(\frac{1}{4},-1\right)[/latex], [latex]\left(1,0\right)[/latex], and [latex]\left(4,1\right)[/latex].Label the points [latex]\left(\frac{1}{4},-2\right)[/latex], [latex]\left(1,0\right)[/latex], and [latex]\left(4,\text{2}\right)[/latex].The domain is [latex]\left(0,\infty \right)[/latex], the range is [latex]\left(-\infty ,\infty \right)[/latex], and the vertical asymptote is x = 0.Sketch a graph of [latex]f\left(x\right)=\frac{1}{2}{\mathrm{log}}_{4}\left(x\right)[/latex] alongside its parent function. Include the key points and asymptote on the graph. Where k=the horizontal stretch/compression; if k<0, the functions has undergone a horizontal reflection across the y-axis. The lesson Graphing Tools: Vertical and Horizontal Scaling in the Algebra II curriculum gives a thorough discussion of horizontal and vertical stretching and shrinking. For example, look at the graph in the previous example. 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. Let’s go through the horizontal transformations.

The graph approaches x = –3 (or thereabouts) more and more closely, so x = –3 is, or is very close to, the vertical 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. You can transform any function into a related function by shifting it horizontally or vertically, flipping it over (reflecting it) horizontally or vertically, or stretching or shrinking it horizontally or vertically.