4 Vertical asymptotes at x 3 and 6 x 5 x intercepts 5 0 and 4 0 y intercept 0 9

4 vertical asymptotes at x 3 and 6 x 5 x intercepts 5

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4. Vertical asymptotes at x= -3 and 6 = x 5. x-intercepts: (-5, 0) and (4, 0); y-intercept: (0, 9 10 ) 6. Looking at the equation it is not clear whether the function has any local maxima or minima. 7. As ± x , the function acts like 2 2 x x y = and its graph approaches the line y= 1. Horizontal asymptote: y = 1. Here is how the function looks on the graph.
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MHF 4U Unit 7: RATIONAL FUNCTIONS 17 Curve Sketching Here is a check-list of the things to consider when you make a sketch of the graph ( ) x f y = . 1. Factor the numerator and denominator (into linear factors if possible). Simplify. 2. Find the domain of ( ) x f . 3. Determine where the function is negative and where positive. 4. Find the points of discontinuity and their types – vertical asymptotes or donut holes. 5. Find the x- and y-intercepts. 6. Find the local maxima and local minima of the function. (Later you will learn how to do this. For now use your graphing calculator.) 7. Determine the end behaviour of the function and see whether the function has any horizontal or oblique asymptotes. 8. Examine the symmetry of the curve with respect to the y-axis and with respect to the origin, i.e. whether the function is even or odd. pg. 272 # 1, 2 pg. 273 # 5 pg. 274 # 9, 14 Assignment C: GRAPHS OF RATIONAL FUNCTIONS
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