# 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 m^{2}.

**5. **$5387.50

**6. a.** m

** b.** sec