Cycle 1 - Lesson 10 – Extra Practice – Rational and Logarithmic Functions
EXTRA PRACTICE QUESTIONS 1.
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11.
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Skills checklist: o identify key features (domain, range, asymptotes, intercepts, end behaviour) on a graph and make connections with the equation of a rational or logarithmic function o write a possible equation for a rational function with the help of technology and by substituting asymptotes and another known point o recognize the relationship between an exponential function its inverse (the corresponding logarithmic function) o identify the parameters of a rational or logarithmic function and describe them in terms of transformations of the basic graph ANSWERS to practice questions 1.
A
2.
a) f(x) 0 b) f(x) 0 c) f(x) +∞ d) f(x) -∞
3.
a) f(x) = 1/(x+2) b) f(x) = 1/(x+4)(x-3)
4.
Domain: {x E R , x ≠ -3, 3} Range: {x E R , x ≠ -3, 3} No x-intercepts y-intercept (0, -1/9) Asymptotes: x = -3, x = 3, y = 0
5.
Domain: x E R Range: {y E R, y < 0} No x-intercepts y-intercept (0, -2) Asymptote y = 0
9.
Domain: {xER, x<0} Range: {y E R} Asymptote: x = 0
10.
vert. comp by 1/2 reflection in y-axis horiz. trans. left 3 vert. trans. up 6 Domain: {xER, x<-3} Range: {y E R} Asymptote: x = -3
6.
Yes, 1/f(x) always has a horizontal asymptote y = 0 (but not necessarily a vertical asymptote)
7.
C
8.
Domain: {x E R, x > 5}, Range {y E R} Asymptote: x = 5
C1-L10 - Extra practice with Rationals and Logarithms.pdf ...
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State the restrictions on the values for each variable. 1. Solve for x in each equation. a). 3 7. + = x b) 5. 4. = x c) 3 5 3. 0. -. = x d). 2. 24. -. = x. 2. Solve and verify. a) 7. 1 15. + = x b). 2. 1. 1. + - = y y c) 8. 1. 5. -. + = v d) 5 2. 2 1
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