Graphing exponentials with vertical transformations and base>1

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Xiaodan Leng 5 years, 8 months ago

Created this as a copy of Graphing exponentials with vertical transformations and base>1 .

Name	Status	Author	Last Modified
Graphing exponentials of the form y=b^x with b>1	Ready to use	Ben Brawn	07/03/2025 05:47
Graphing exponentials of the form y=b^x with 0<b<1	Ready to use	Ben Brawn	07/03/2025 05:47
Graphing exponentials with vertical transformations and base>1	Ready to use	Ben Brawn	07/03/2025 05:47
Graphing exponentials with horizontal and vertical transformations and base>1	Ready to use	Ben Brawn	07/03/2025 05:47
Graphing logarithms of the form y=log_{b}(x) with b>1	Ready to use	Ben Brawn	03/03/2025 00:25
Graphing logarithms with vertical transformations and base>1	Ready to use	Ben Brawn	03/03/2025 00:25
Graphing logarithms with horizontal and vertical transformations and base>1	Ready to use	Ben Brawn	03/03/2025 00:25
Jamie's copy of Graphing logarithms of the form y=log_{b}(x) with b>1	draft	Jamie Wood	19/09/2017 12:36
Jamie's copy of Graphing logarithms with vertical transformations and base>1	draft	Jamie Wood	19/09/2017 12:38
Jamie's copy of Graphing exponentials with horizontal and vertical transformations and base>1	draft	Jamie Wood	19/09/2017 13:33
Jamie's copy of Graphing exponentials with vertical transformations and base>1	draft	Jamie Wood	19/09/2017 13:29
Jamie's copy of Graphing logarithms with horizontal and vertical transformations and base>1	draft	Jamie Wood	19/09/2017 12:43
Jamie's copy of Graphing exponentials of the form y=b^x with b>1	draft	Jamie Wood	19/09/2017 13:07
Maria's copy of Graphing exponentials of the form y=b^x with b>1	draft	Maria Aneiros	25/05/2019 08:02
Exam04 - Exponentials	draft	Michael Proudman	07/12/2021 09:54
nuExam04 - Exponentials	draft	Michael Proudman	07/12/2021 09:54
Graphing exponentials with vertical transformations and base>1	draft	Xiaodan Leng	11/07/2019 01:13
Graphing exponentials with vertical transformations and base>1	draft	Xiaodan Leng	11/07/2019 01:26
Graphing exponentials with horizontal and vertical transformations and base>1	draft	Xiaodan Leng	11/07/2019 01:27
Graphing exponentials of the form y=b^x with 0<b<1	draft	Xiaodan Leng	11/07/2019 01:31
Graphing exponentials of the form y=b^x with b>1	draft	Xiaodan Leng	11/07/2019 01:32
Graphing logarithms with horizontal and vertical transformations and base>1	draft	Xiaodan Leng	11/07/2019 02:17
Graphing logarithms of the form y=log_{b}(x) with b>1	draft	Xiaodan Leng	11/07/2019 02:18
Graphing logarithms with vertical transformations and base>1	draft	Xiaodan Leng	11/07/2019 02:18

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Question statement

The following questions will gauge your understanding of exponentials and how to graph them.

The exponential you will be working with for this question is \[y=\simplify{{a}{b}^x+{c}}.\]

Give any introductory information the student needs.

			Name	Type	Generated Value

b	integer	7
a	integer	-2
c	integer	2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..10)

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Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Choose one from a list
Part d) Gap-fill
1. Gap Number entry
  Add
Part e) Choose one from a list

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

The $y$-intercept of $y=\simplify{{a}{b}^x+{c}}$ is the point $\large($Gap 0., Gap 1.$\large)$.

Advice

a) To find the $y$-intercept, substitute $x=0$ into the equation: $y=\simplify[!collectNumbers,basic]{{a}{b}^0+{c}}=\simplify[!collectNumbers, basic]{{a}+{c}}=\var{a+c}$. Therefore, the $y$-intercept is the point $(0,\var{a+c})$.

b) Substitute $x=1$ into the equation: $y=\simplify[!collectNumbers, basic]{{a}{b}^1+{c}}=\var{a*b+c}$. Therefore, another easily found point is $(1,\var{a*b+c})$.

c) As $x$ gets larger and larger (increases without bound, or approaches infinity) $y=\simplify{{a}{b}^x+{c}}$ gets smaller and smaller (decreases without bound, or approaches negative infinity). larger and larger (increases without bound, or approaches infinity).

d) An asymptote is a line or curve that approaches a given curve arbitrarily closely. Because as $x$ gets very small, $\simplify{{b}^x}$ gets close to zero, $\simplify{{a}{b}^x}$ gets close to zero, and $\simplify{{a}{b}^x+{c}}$ gets close to $\var{c}$. That is, for the curve $\simplify{{a}{b}^x+{c}}$ the smaller $x$ gets, the closer $y$ gets to $\var{c}$. In other words as $x$ approaches negative infinity, $y$ approaches $\var{c}$. So the asymptote for $y=\simplify{{a}{b}^x+{c}}$ is the line $y=\var{c}$.

e) Given all the information above, it should be clear that the graph should look like

{graph1(1)}

Give a worked solution to the whole question.

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Part	Test	Passed?
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Graphing exponentials with vertical transformations and base>1

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Graphing exponentials with vertical transformations and base>1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`