Graphing exponentials with vertical transformations and base>1

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Ben Brawn

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7 years, 10 months ago

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Ben Brawn 7 years, 10 months ago

Gave some feedback: Ready to use

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Ben Brawn 7 years, 10 months ago

Created this as a copy of Graphing exponentials of the form y=b^x with b>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	8
a	integer	3
c	integer	1

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..10)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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1. Step Information only
Part b) Gap-fill
1. Gap Number entry
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Part c) Choose one from a list
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Part d) Gap-fill
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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 $y=\simplify[!noleadingminus]{{a}{b}^x+{c}}$ 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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This question is used in the following exams:

Mid Unit Revision by Mike Phipps in Maths for STEM.
Graphing and Polynomials by Chris Templet in Chris's workspace.
Graphing exponentials by Ben Brawn in Graphing and Polynomials.

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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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Ben Brawn 7 years, 10 months ago

Ben Brawn 7 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Graphing exponentials with vertical transformations and base>1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben Brawn 7 years, 10 months ago

Ben Brawn 7 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`