3.5. Practice question answers
Chapter 3 practice question answers
3.1. Introduction to Functions
1. Yes
2. No
3. Yes
4. Q = g(4) = 6
5. x = 0 or x = 2
6. a. g(5) = 1
b. m = 8
3.2. Domain and Range
1. Domain; y = years [1960,2010] ; Range, p = population, [100,1400]
2. a. Values that are less than or equal to -2, or values that are greater than or equal to -1 and less than 3
b. {x | x ≤ -2 or -1 ≤ x < 3}
c. (-∞, -2] ∪ [-1, 3)
3. Domain; y = years, [1952,2002] ; Range, p = population in millions, [40,88]
4.
A reasonable domain should be whole numbers 0 to (answers may vary), e.g. [0,23]. A reasonable range should be $0 – (answers may vary), e.g. [0,1524].
5. a. {x | 2008 ≤ x ≤ 2018}, [2008, 2018]
b. {x | 16.1 ≤ x ≤ 88.4}, [16.1, 88.4]
3.3. Rates of Change and Behaviour of Graphs
1. $0.264 dollars per year.
2. Average rate of change = .
3.
4. Based on the graph, the local maximum appears to occur at (-1, 28), and the local minimum occurs at (5,-80). The function is increasing on (-∞, -1)∪(5, ∞) and decreasing on (-1, 5).
5. a. -0.59 per 100,000
b. 6
c. 2010, 2014, and 2017
3.4. Quadratic Functions
1. in standard form; in vertex form.
2. a. Vertex is a minimum value (opens upwards).
b. Vertex is a maximum value (opens downwards).
3.
4. Two sides with lengths of 8 m and the longer side with a length of 16 m will give a maximum dimension of 128 m2.
5. $5387.50
6. a. m
b. sec