Finding Vertical Asymptotes In Exercises 75–-82, find the vertical asymptotes (if any) of the
graph of the function.
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- Graph the functions on the same screen using the given viewing rectangle. Viewing rectangle [−8, 8] by [−6, 6](a) y = |x| (b) y = −|x| (c) y = −4|x| (d) y = −4|x − 2| How is the graph in part (b) related to the graph in part (a)? If a graph is not supposed to be stretched or shrunk, enter "1" in the corresponding box on the right. If a graph is not supposed to be shifted in some direction, enter "0" in the corresponding box on the right. Reflect? Reflect across the x-axis Reflect across the y-axis Do not reflect Stretch/Shrink vertically? stretch vertically shrink vertically neither stretch nor shrink vertically by a factor of Stretch/Shrink horizontally? stretch horizontally shrink horizontally neither stretch nor shrink horizontally by a factor of Shift up/down? shift up shift down do not shift up or down units Shift left/right? shift left shift right do not shift left or right units How is the graph in part (c) related to the…arrow_forward(a) Sketch the graph for the equation f(x) = x³ – 2x2 + x + 1. In the graph, show the local extrema of f(x), the intervals on which the graph of f (x) is concave upward or is downward, and the coordinate of the point of inflection. Sketching only the graph will not giving you the mark. Demonstrate how you get the answer.arrow_forwardUse a graphing utility to graph the function and determine the slant asymptote of the graph analytically. Zoom out repeatedly and describe how the graph on the display appears to change. Why does this occur? f(x) = (−x2 − 3x − 1)/(x − 2)arrow_forward
- (b)Explain even and odd function with example? Determine whether the f(x) = (c) Graph f(x) -2(x+ 2) -1 using graphing technique 3r is even or not.arrow_forwardUse the graph of f to sketch each graph. (a) y = f(−x) (b) y = f(x) + 4 (c) y = 2f(x) (d) y = −f(x − 4) (e) y = f(x) − 3 (f ) y = −f(x) − 1 (g) y = f(2x)arrow_forwardA 48-gallon barrel contains a mixture with a concentration of 33% sodium chloride. You remove x gallons of this mixture and replace it with 100% sodium chloride. (a) Write the amount A of sodium chloride in the final mixture as a function of x.A(x) = (b) Use a graphing utility to graph the concentration function. What is the domain of the function? (Enter your answer using interval notation.) (c) Approximate (accurate to one decimal place) the value of x when the final mixture is 60% sodium chloride.x = ____ galarrow_forward
- The graph of f(x) = x2_______ to the left and_______ to the right.arrow_forwardFind the vertical asymptotes (if any) of the graph of the function f(x) = 3/(x2 + x − 2)arrow_forward(a) Graph y = √x Show coordinates of at lease TWO points on the graph. (b) Write (in words) what you do to transform the graph in (a) to obtain the graph of y = √(x + 2). Then graph it . Show coordinates of at lease TWO points on the graph.arrow_forward
- Use a graphing utility to graph the function and determine the slant asymptote of the graph analytically. Zoom out repeatedly and describe how the graph on the display appears to change. Why does this occur? f(x) = −(x3 − 2x2 + 2)/2x2arrow_forwardThe graph of f(x): (a) Determine f(2). (b) Estimate the x values such that f(x) = 5 (c) Estimate the x-interval in which f(x) is decreasing. I notation. (d) What are the coordinates of the relative maximum? (e) What are the coordinates of the y-intercept? (fH) What are the coordinates of the x-intercepts?arrow_forwarddetermine the vertical asymptote of the functions, if anyarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage