Difference between revisions of "005 Sample Final A, Question 17"

Latest revision as of 10:48, 2 June 2015

Question Graph the following function,

f(x)=\log _{2}(x+1)+2

Make sure to label any asymptotes, and at least two points on the graph.

Foundations
1) What is the basic graph of $f(x)=\log _{2}(x+1)+2$ ?
2) How is the graph $g(x)=x^{3}+2$ obtained from $f(x)=x^{3}$ ?
3) How is the graph $g(x)=(x+1)^{2}$ obtained from $f(x)=x^{2}$ ?
Answer:
1) The basic graph is $y=\log _{2}(x)$ .
2) The graph of $g(x)$ is obtained by shifting the graph of $f(x)$ up 2 unit.
3) The graph of $g(x)$ is obtained by shifting the graph of $f(x)$ to the left by 1 unit.

Solution:

Step 1:
We start with the basic graph of $g(x)=\log _{2}(x)$ .
To get the graph of $f(x)$ from $g(x)$ , we shift the graph of $g(x)$ up 2 and to the left by 1.

Step 2:
Two points on the graph are (0, 2) and (1, 3). There is a vertical asymptote at $x=-1$ .

Final Answer:
Two points on the graph are (0, 2) and (1, 3). There is a vertical asymptote at $x=-1$ .

Return to Sample Exam

@@ Line 4: / Line 4: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answers
+! Foundations
 |-
-|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>
+|1) What is the basic graph of <math> f(x) = \log_2(x+1) + 2</math>?
 |-
-|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.
+|2) How is the graph <math>g(x)=x^3 + 2</math> obtained from <math>f(x)=x^3</math>?
 |-
-|c) False. <math>y = x^2</math> does not have an inverse.
+|3) How is the graph <math>g(x)=(x+1)^2</math> obtained from <math>f(x)=x^2</math>?
 |-
-|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
+|Answer:
 |-
-|e) True.
+|1) The basic graph is <math>y=\log_2(x)</math>.
 |-
-|f) False.
+|2) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> up 2 unit.
+|-
+|3) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> to the left by 1 unit.
+|}
+Solution:
+{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 1:
+|-
+|We start with the basic graph of <math>g(x)=\log_2(x)</math>.
+|-
+|To get the graph of <math>f(x)</math> from <math>g(x)</math>, we shift the graph of <math>g(x)</math> up 2 and to the left by 1.
+|}
+{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 2:
+|-
+|Two points on the graph are (0, 2) and (1, 3). There is a vertical asymptote at <math>x = -1</math>.
+|}
+{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+! Final Answer:
+|-
+|Two points on the graph are (0, 2) and (1, 3). There is a vertical asymptote at <math>x = -1</math>.
+|-
+|
+[[File:5_Sample_Final_17.png]]
 |}
 [[005 Sample Final A|'''<u>Return to Sample Exam</u>''']]

Difference between revisions of "005 Sample Final A, Question 17"

Latest revision as of 10:48, 2 June 2015

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