MathAdmin at 17:15, 2 June 2015

2015-06-02T17:15:31Z

MathAdmin: Created page with " Describe how the graph of $f(x) = 3^{(x+1)} - 2$ can be obtained from a basic graph. Then sketch the graph...."

2015-06-01T05:47:28Z

Created page with "<span class="exam"> Describe how the graph of <math style="vertical-align:-17%"> f(x) = 3^{(x+1)} - 2</math> can be obtained from a basic graph. Then sketch the graph...."

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<span class="exam"> Describe how the graph of <math style="vertical-align:-17%"> f(x) = 3^{(x+1)} - 2</math>  can be obtained from a basic graph. Then sketch the graph. Provide at least two ordered pairs, and the equation of any asymptote.
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
|-
|1) What is the basic graph of <math> f(x) = 3^{(x+1)} - 2</math>?
|-
|2) How is the graph <math>g(x)=x+1</math> obtained from <math>f(x)=x</math>?
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|3) How is the graph <math>g(x)=(x-3)^2</math> obtained from <math>f(x)=x^2</math>?
|-
|Answer:
|-
|1) The basic graph is <math>y=3^x</math>.
|-
|2) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> up 1 unit.
|-
|3) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> to the right by 3 units.
|}

Solution:

{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
|-
|We start with the basic graph of <math>g(x)=3^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> down 2 and to the left by 1.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
|Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at <math>y=-2</math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
|-
|To get the graph of <math>f(x)</math> from <math>3^x</math>, we shift the graph of <math>3^x</math> down 2 and to the left by 1.
|-
|Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at <math>y=-2</math>
|}

[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

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 |-
 |Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at <math>y=-2</math>
 |}
 [[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

004 Sample Final A, Problem 5 - Revision history

MathAdmin at 17:15, 2 June 2015

MathAdmin: Created page with " Describe how the graph of f(x) = 3^{(x+1)} - 2 can be obtained from a basic graph. Then sketch the graph...."

MathAdmin: Created page with " Describe how the graph of $f(x) = 3^{(x+1)} - 2$ can be obtained from a basic graph. Then sketch the graph...."