{"id":53,"date":"2020-02-07T13:20:27","date_gmt":"2020-02-07T18:20:27","guid":{"rendered":"https:\/\/pressbooks.library.torontomu.ca\/pohmath\/chapter\/3-4-practice-question-answers\/"},"modified":"2023-11-27T14:19:24","modified_gmt":"2023-11-27T19:19:24","slug":"3-4-practice-question-answers","status":"publish","type":"chapter","link":"https:\/\/pressbooks.library.torontomu.ca\/pohmath\/chapter\/3-4-practice-question-answers\/","title":{"raw":"3.5. Practice question answers","rendered":"3.5. Practice question answers"},"content":{"raw":"[Latexpage]\n

Chapter 3 practice question answers<\/h1>\n \n
\n

3.1. Introduction to Functions<\/strong><\/p>\n\n<\/header>\n

\n
<\/div>\n
\n

1.<\/strong> Yes<\/p>\n

2.<\/strong> No<\/p>\n

3.<\/strong> Yes<\/p>\n

4.<\/strong> Q<\/em> = g(4) = 6<\/p>\n

5.<\/strong> x<\/em> = 0 or x<\/em> = 2<\/p>\n

6. <\/strong>a.<\/strong> g(5) = 1<\/p>\n

\u00a0 \u00a0 b.<\/strong> m<\/em> = 8<\/p>\n \n\n<\/div>\n<\/div>\n<\/div>\n \n

\n

3.2. Domain and Range<\/strong><\/p>\n\n<\/header>\n

\n\n1.<\/strong> Domain; y<\/em> = years [1960,2010] ; Range, p<\/em> = population, [100,1400]\n\n2. <\/strong>a.<\/strong> Values that are less than or equal to -2, or values that are greater than or equal to -1 and less than 3\n\n\u00a0 \u00a0 b.<\/strong> {x<\/em> | x<\/em> \u2264 -2 or -1 \u2264 x<\/em> < 3}\n\n\u00a0 \u00a0 c.<\/strong> (-\u221e, -2] \u222a [-1, 3)\n\n3.<\/strong> Domain; y <\/em>= years, [1952,2002] ; Range, p <\/em>= population in millions, [40,88]\n\n4.<\/strong> $T(c)=\\begin{cases}\n\n89.5c \\quad if \\quad c\\le10\\\\\n\n895+33(c-10)\\quad if \\quad 10<c\\le18 \\quad Tuition,\\;T,\\;as\\;a\\;function\\;of\\;credits,\\;c.\\\\\n\n1159+73(c-18)\\quad if \\quad c>18\\\\\n\n\\end{cases}$\n\nA reasonable domain should be whole numbers 0 to (answers may vary), e.g. [0,23]. A reasonable range should be \\$0 \u2013 (answers may vary), e.g. [0,1524].\n\n5.\u00a0 <\/strong>a.<\/strong> {x<\/em> | 2008 \u2264 x<\/em> \u2264 2018}, [2008, 2018]\n\n\u00a0 \u00a0 \u00a0<\/strong>b.<\/strong> {x<\/em> | 16.1 \u2264 x<\/em> \u2264 88.4}, [16.1, 88.4]\n\n<\/div>\n<\/div>\n \n
\n

3.3. Rates of Change and Behaviour of Graphs<\/strong><\/p>\n\n<\/header>\n

\n\n1.<\/strong> \\$0.264 dollars per year.\n\n2.<\/strong> Average rate of change = $\\frac{1}{2}$.\n\n3.<\/strong> $\\3a^2+3ah+h^2$\n\n4.<\/strong> 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 (-\u221e, -1)\u222a(5, \u221e) and decreasing on (-1, 5).\n\n5.<\/strong> \u00a0a.\u00a0<\/strong>-0.59 per 100,000\n\n\u00a0 \u00a0 \u00a0b. <\/strong>6\n\n\u00a0 \u00a0 \u00a0c. <\/strong>2010, 2014, and 2017\n\n<\/div>\n<\/div>\n \n
\n

3.4. Quadratic Functions<\/strong><\/p>\n\n<\/header>\n

\n\n1.<\/strong>\u00a0$g(x)=x^2-6x+13$ in standard form; $g(x)=(x-3)^2+4$ in vertex form.<\/span>\n\n2. a.<\/strong> Vertex is a minimum value (opens upwards).\n\n\u00a0 \u00a0 b.<\/strong> Vertex is a maximum value (opens downwards).\n\n3. <\/strong>$f(x)=-3(x-1)^2-9$\n\n4.<\/strong> 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<\/sup>.\n\n5. <\/strong>\\$5387.50\n\n6. a.<\/strong> $65.625$ m<\/span>\n\n\u00a0 \u00a0 b.<\/strong> $\\approx 6.16$ sec\n\n<\/div>\n<\/div>\n ","rendered":"

Chapter 3 practice question answers<\/h1>\n

 <\/p>\n

\n
\n

3.1. Introduction to Functions<\/strong><\/p>\n<\/header>\n

\n
<\/div>\n
\n

1.<\/strong> Yes<\/p>\n

2.<\/strong> No<\/p>\n

3.<\/strong> Yes<\/p>\n

4.<\/strong> Q<\/em> = g(4) = 6<\/p>\n

5.<\/strong> x<\/em> = 0 or x<\/em> = 2<\/p>\n

6. <\/strong>a.<\/strong> g(5) = 1<\/p>\n

\u00a0 \u00a0 b.<\/strong> m<\/em> = 8<\/p>\n

 <\/p>\n<\/div>\n<\/div>\n<\/div>\n

 <\/p>\n

\n
\n

3.2. Domain and Range<\/strong><\/p>\n<\/header>\n

\n

1.<\/strong> Domain; y<\/em> = years [1960,2010] ; Range, p<\/em> = population, [100,1400]<\/p>\n

2. <\/strong>a.<\/strong> Values that are less than or equal to -2, or values that are greater than or equal to -1 and less than 3<\/p>\n

\u00a0 \u00a0 b.<\/strong> {x<\/em> | x<\/em> \u2264 -2 or -1 \u2264 x<\/em> < 3}<\/p>\n

\u00a0 \u00a0 c.<\/strong> (-\u221e, -2] \u222a [-1, 3)<\/p>\n

3.<\/strong> Domain; y <\/em>= years, [1952,2002] ; Range, p <\/em>= population in millions, [40,88]<\/p>\n

4.<\/strong> \"T(c)=\begin{cases}<\/p>\n

A reasonable domain should be whole numbers 0 to (answers may vary), e.g. [0,23]. A reasonable range should be $0 \u2013 (answers may vary), e.g. [0,1524].<\/p>\n

5.\u00a0 <\/strong>a.<\/strong> {x<\/em> | 2008 \u2264 x<\/em> \u2264 2018}, [2008, 2018]<\/p>\n

\u00a0 \u00a0 \u00a0<\/strong>b.<\/strong> {x<\/em> | 16.1 \u2264 x<\/em> \u2264 88.4}, [16.1, 88.4]<\/p>\n<\/div>\n<\/div>\n

 <\/p>\n

\n
\n

3.3. Rates of Change and Behaviour of Graphs<\/strong><\/p>\n<\/header>\n

\n

1.<\/strong> $0.264 dollars per year.<\/p>\n

2.<\/strong> Average rate of change = \"\frac{1}{2}\".<\/p>\n

3.<\/strong> \"\3a^2+3ah+h^2\"<\/p>\n

4.<\/strong> 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 (-\u221e, -1)\u222a(5, \u221e) and decreasing on (-1, 5).<\/p>\n

5.<\/strong> \u00a0a.\u00a0<\/strong>-0.59 per 100,000<\/p>\n

\u00a0 \u00a0 \u00a0b. <\/strong>6<\/p>\n

\u00a0 \u00a0 \u00a0c. <\/strong>2010, 2014, and 2017<\/p>\n<\/div>\n<\/div>\n

 <\/p>\n

\n
\n

3.4. Quadratic Functions<\/strong><\/p>\n<\/header>\n

\n

1.<\/strong>\u00a0\"g(x)=x^2-6x+13\" in standard form; \"g(x)=(x-3)^2+4\" in vertex form.<\/span><\/p>\n

2. a.<\/strong> Vertex is a minimum value (opens upwards).<\/p>\n

\u00a0 \u00a0 b.<\/strong> Vertex is a maximum value (opens downwards).<\/p>\n

3. <\/strong>\"f(x)=-3(x-1)^2-9\"<\/p>\n

4.<\/strong> 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<\/sup>.<\/p>\n

5. <\/strong>$5387.50<\/p>\n

6. a.<\/strong> \"65.625\" m<\/span><\/p>\n

\u00a0 \u00a0 b.<\/strong> \"\approx 6.16\" sec<\/p>\n<\/div>\n<\/div>\n

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