Cycle 1 - Lesson 10 – Extra Practice – Rational and Logarithmic Functions

EXTRA PRACTICE QUESTIONS 1.

4.

5.

2.

3.

7.

11.

10.

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

11. a) b) c) d)

27=128 bx=n 35=243 b19=4