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. T(c)=\begin{cases}  89.5c \quad if \quad c\le10\\  895+33(c-10)\quad if \quad 10<c\le18 \quad Tuition,\;T,\;as\;a\;function\;of\;credits,\;c.\\  1159+73(c-18)\quad if \quad c>18\\  \end{cases}

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. \frac{\$3.01-\$1.69}{5\;years}=\frac{\$1.32}{5\;years}= 0.264 dollars per year.

2. Average rate of change = \frac{f(9)-f(1)}{9-1}=\frac{(9-2\sqrt{9})}{9-1}=\frac{(3)-(-1)}{9-1}=\frac{4}{8}=\frac{1}{2}.

3. \frac{f(a+h)-f(a)}{(a+h)-a}=\frac{((a+h)^3+2)-(a^3+2)}{h}

=\frac{a^3+3a^2h+3ah^2+h^3+2-a^3-2}{h}=\frac{3a^2h+3ah^2+h^3}{h}

=\frac{h(3a^2+3ah+h^2)}{h}=3a^2+3ah+h^2

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. The path passes through the origin with vertex at (-4, 7).

h(x)=-\frac{7}{16}(x+4)^2+7& .

To make the shot, h(-7.5) would need to be about 4.

h(-7.5) ≈ 1.64; he doesn’t make it.

2. g(x)=x^2-6x+13 in standard form; g(x)=(x-3)^2+4 in vertex form.

3. a. Vertex is a minimum value (opens upwards).

    b. Vertex is a maximum value (opens downwards).

4.f(x)=-3(x-1)^2-9

5. $5387.50

6. a. 65.625 m

    b. \approx 6.16 sec