Difference between revisions of "005 Sample Final A, Question 1"

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(Created page with "'''Question''' Please circle either true or false,<br>     a. (True/False)In a geometric sequence, the common ratio is always positive. <br>   &n...")
 
 
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'''Question''' Please circle either true or false,<br>
 
'''Question''' Please circle either true or false,<br>
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&nbsp;&nbsp;&nbsp;&nbsp;a. (True/False)In a geometric sequence, the common ratio is always positive. <br>
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&nbsp;&nbsp;&nbsp;&nbsp;a. (True/False) In a geometric sequence, the common ratio is always positive. <br>
 
&nbsp;&nbsp;&nbsp;&nbsp;b. (True/False) A linear system of equations always has a solution. <br>
 
&nbsp;&nbsp;&nbsp;&nbsp;b. (True/False) A linear system of equations always has a solution. <br>
 
&nbsp;&nbsp;&nbsp;&nbsp;c. (True/False) Every function has an inverse. <br>
 
&nbsp;&nbsp;&nbsp;&nbsp;c. (True/False) Every function has an inverse. <br>
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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! Foundations
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! Final Answers
 
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|1) How would you find the inverse for a simpler function like <math>f(x) = 3x + 5</math>?
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|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
 
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|2) How are <math>log_3(x)</math> and <math>3^x</math> related?
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|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
 
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|Answers:
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|c) False. <math>y = x^2</math> does not have an inverse.
 
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|1) you would replace f(x) by y, switch x and y, and finally solve for y.
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|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
 
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|2) By stating <math>y = \log_3(x)</math> we also get the following relation <math>x = 3^y</math>
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|e) True. The domain of <math>\tan^{-1}(x)</math> is the range of <math>\tan(x)</math>
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|f) False. The domain of <math>\log_a(x)</math> is the range of <math>e^x</math>
 
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[[005 Sample Final A|<u>'''Return to Sample Exam</u>''']]
 
[[005 Sample Final A|<u>'''Return to Sample Exam</u>''']]

Latest revision as of 22:45, 4 May 2015

Question Please circle either true or false,
    a. (True/False) In a geometric sequence, the common ratio is always positive.
    b. (True/False) A linear system of equations always has a solution.
    c. (True/False) Every function has an inverse.
    d. (True/False) Trigonometric equations do not always have unique solutions.
    e. (True/False) The domain of is all real numbers.
    f. (True/False) The function is defined for all real numbers.


Final Answers
a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_n = (-a)^n}
b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
c) False. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = x^2} does not have an inverse.
d) True. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle cos^2(x) - cos(x) = 0} has multiple solutions.
e) True. The domain of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tan^{-1}(x)} is the range of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tan(x)}
f) False. The domain of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \log_a(x)} is the range of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^x}

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