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1. Given the following equations, determine each of the following. f(x): 3x1 4x + 1 Domain x-intercept(s) y-intercept(s) Horizontal Asymptote(s) Vertical Asymptote(s) [10] g(x) = (x-3)(x + 4)(x + 1)
2. Given the following graph, determine the following: Domain y-intercept Equation of all asymptotes Interval(s) where the function is positive Interval(s) where the function is increasing Interval(s) where the function is positive and decreasing. (0.-0.333) (1.-0.25) [9]
-5 (0.-0.333) (1.-0.25) -5 5
3. Determine algebraically whether the following functions are odd, even, or neither. f(x) = x³ - 2x b) f(x)= a) (x-3)³
4. Describe how the graph of y=-3f[2(x + 5)]- 4 can be obtained from the graph of f(x) = x³. Be sure to use full sentences when describing the transformations.
²-16 5. Consider the function. f(x) = Determine the following key features of the function: i) domain and range iii) equations of any asymptotes v) Sketch the graph. ii) intercepts [12] iv) interval(s) where the function is decreasing
2x-12 x+1 Solve algebraically. Use either a number line or interval notation to state the final solution. Be sure to include a behaviour chart to show your work. [5] x+7 x+3
Determine an equation for the family of cubic functions, in simplified form, with the following zeros: 3 ± √2 and -5.
8. Use the information below to sketch the function. • There is a horizontal asymptote at /(x)=1 The denominator of the function is x²-x-2 There is a y-intercept at 4. • f(-2) = f(4) = 0 f(-6) 1 . f(x) <0 when -2 < x < -1,2 < x < 4 f(x)>0 when x < -2,-1 < x < 2, x > 4 ●