Chapter 8

8 Getting Started
Study
Aid
• For help, see the Review of
Essential Skills found at the
Nelson Advanced Functions
website.
Question Appendix
1, 2, 3 R-1
4, 8 R-7, R-8
6, 7 R-7
SKILLS AND CONCEPTS You Need
1. Rewrite each expression in an equivalent form, and then evaluate.
a) c) e) 2121 1 2
36 1 2
5 22
b) d) f) a 8 2 2
27 b 3
125 1 3
11 0
2. Simplify each expression, and then evaluate.
10 9
a) c) e) (8 1 3 )
2
(3 5 )(3 2 )
10 6
(4 3 4
b) d) f)
)(41 4
(7 6 )(7 23 )
(22) )
12 (22) 210 4 1 2
7 21
3. Simplify.
a) c) e) (2d 4 ) a c 2
(16x 6 ) 1 2
(2m) 3 d b 21
x 5 y 2
b) (a 4 b 5 ) 22 d) f) a(x 3 ) 21 3b
x 2 y
4. Sketch a graph of each of the following exponential functions. State
the domain, range, y-intercept, and the equation of the horizontal
asymptote of each function.
a) b) y 5 a 1 x
y 5 2 x
c) y 5 3 2x 2 2
2 b
5. a) Determine the equation of the inverse of each of the following
functions.
i) f (x) 5 3x 2 6 iii) f (x) 5 6x 3
ii) f (x) 5 x 2 2 5 iv) f (x) 5 (x 2 4) 2 1 3
b) Which of the inverses you found in part a) are also functions?
6. A bacteria culture doubles every 4 h. If there are 100 bacteria in the
culture initially, determine how many bacteria there will be after
a) 12 h c) 3.5 days
b) 1 day d) 1 week
7. The population of a town is declining at a rate of 1.2% per year. If the
population was 15 000 in 2005, what will the population be in 2020?
8. Use a table like this to compare the graphs of y 5 3(2 x ) and y 5 3Q 1 2 Rx .
Similarities
Differences
446 Getting Started
NEL