Learning Target: I can sketch the graphs of rational functions without a calculator. a. Determine the equation(s) of the asymptotes.
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1 Learning Target: I can sketch the graphs of rational functions without a calculator Consider the graph of y= f(x), where f(x) = 3x 3 (x+2) 2 a. Determine the equation(s) of the asymptotes. b. Find the axes intercepts. c. Find f (x) and determine the position and nature of any stationary points. Note: You will have to simplify your derivative. d. Determine the intervals for which the function is increasing and/or decreasing.
2 Learning Target : I can sketch the graphs of rational functions without a calculator Consider the graph of y= f(x), where f(x) = 2x x 2 4 a. Determine the equation(s) of the asymptotes. b. Find the axes intercepts. c. Find f (x) and determine the position and nature of any stationary points. Note: You will have to simplify your derivative. d. Determine the intervals for which the function is increasing and/or decreasing.
3 Learning Target : I can sketch the graphs of functions without a calculator Consider f(x) = x 3-6x x + 1. a. Find f (x) and determine the position and nature of any stationary point(s). b. Determine the intervals for which the function is increasing and/or decreasing for f(x) using f (x). c. Determine the intervals for which the function is concave up and/or down for f(x) using f (x). d. Determine the position any inflection points.
4 Learning Target : I can sketch the graphs of functions without a calculator Consider the graph of y= f(x), where f(x) = x 4 2x 2 4 a. Find f (x) and determine the position and nature of any stationary point(s). b. Determine the intervals for which the function is increasing and/or decreasing for f(x) using f (x). c. Determine the intervals for which the function is concave up and/or down for f(x) using f (x). d. Sketch the function showing all the information above.
5 Learning Target : I can sketch the graphs of functions without a calculator Consider the graph of y= f(x), where f(x) = 3 x a. Find f (x) and determine the position and nature of any stationary point(s). b. Determine the intervals for which the function is increasing and/or decreasing for f(x) using f (x). c. Determine the intervals for which the function is concave up and/or down for f(x) using f (x). d. Determine the position any inflection points.
6 Learning Target: I can answer questions from previous IB exams. 1 Consider f (x) = x 3 + 2x 2 5x. Part of the graph of f is 3 shown below. There is a maximum point at M, and a point of inflexion at N. (a) Find f (x). (b) Find the x-coordinate of M. (c) Find the x-coordinate of N. (d) The line L is the tangent to the curve of f at (3, 12). Find the equation of L in the form y = ax + b. (4) (Total 14 marks) (3) (4) (3)
7 Calculator Learning Target: I can sketch the graphs of functions that may require a calculator. Consider the graph of y= f(x), where f(x) = x 3 4x 2 + 4x a. Find f (x) and determine the position and nature of any stationary point(s). b. Determine the intervals for which the function is increasing and/or decreasing for f(x) using f (x). c. Determine the intervals for which the function is concave up and/or down for f(x) using f (x). d. Determine the position any inflection points.
8 Calculator Learning Target: I can find a missing part of a function using derivatives. Suppose f(x) = x 3 + ax + 2, has a turning point when x = a. Find a. b. Find the position and nature of all stationary points for f(x).
9 Calculator Learning Target: I can answer questions from previous IB exams A curve has equation y = x(x 4) 2. (a) For this curve find (i) the x-intercepts; (ii) the coordinates of the maximum point; (iii) the coordinates of the point of inflexion. (9) (b) Use your answers to part (a) to sketch a graph of the curve for 0 x 4, clearly indicating the features you have found in part (a). (3
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