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

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 $f(x)=\tan ^{-1}(x)$ is all real numbers.
    f. (True/False) The function $\log _{a}(x)$ 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, $a_{n}=(-a)^{n}$
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. $y=x^{2}$ does not have an inverse.
d) True. $cos^{2}(x)-cos(x)=0$ has multiple solutions.
e) True. The domain of $\tan ^{-1}(x)$ is the range of $\tan(x)$
f) False. The domain of $\log _{a}(x)$ is the range of $e^{x}$

Return to Sample Exam

@@ Line 1: / Line 1: @@
 '''Question''' Please circle either true or false,<br>
-&nbsp;&nbsp;&nbsp;&nbsp;a. (True/False)In a geometric sequence, the common ratio is always positive. <br>
+&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;c. (True/False) Every function has an inverse. <br>
@@ Line 9: / Line 9: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Foundations
+! Final Answers
 |-
-|1) How would you find the inverse for a simpler function like <math>f(x) = 3x + 5</math>?
+|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>
 |-
-|2) How are <math>log_3(x)</math> and <math>3^x</math> related?
+|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.
 |-
-|Answers:
+|c) False. <math>y = x^2</math> does not have an inverse.
 |-
-|1) you would replace f(x) by y, switch x and y, and finally solve for y.
+|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
 |-
-|2) By stating <math>y = \log_3(x)</math> we also get the following relation <math>x = 3^y</math>
+|e) True. The domain of <math>\tan^{-1}(x)</math> is the range of <math>\tan(x)</math>
+|-
+|f) False. The domain of <math>\log_a(x)</math> is the range of <math>e^x</math>
 |}
 [[005 Sample Final A|<u>'''Return to Sample Exam</u>''']]

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

Latest revision as of 22:45, 4 May 2015

Navigation menu

Search