Functions

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Don Shearman 11 months, 2 weeks ago

Published this.

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Don Shearman 3 years, 8 months ago

Created this.

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Question statement

Let $\displaystyle{h(x)=\frac{\simplify{{a}*x+{b}}}{\simplify{{c}*x+{d}}}}$ and $k(x)=\simplify{{l}x+{m}}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

f_x	expression	(3x + 2)/(2x + 5)
g_x	expression	9x + -4
comb_n	rational	98/69
comb	list	List of 2 items
a	integer	3
b	integer	2
c	integer	2
d	integer	5
l	integer	9
m	integer	-4
n	integer	4
switch	integer	1
f_xNum	expression	3x + 2
f_xDenom	expression	2x + 5
answer	expression	9((3x + 2)/(2x + 5)) + -4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
substitute(["a":a,"b":b,"c":c,"d":d],expression("(a*x+b)/(c*x+d)"))

JME function reference

Description

Expression for h(x)

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

Can an exam override the value of this variable?

Generated value: `expression`

(3x + 2)/(2x + 5)

← Depends on:

→ Used by:

comb

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Choose one from a list
Part c) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

Evaluate Leave your answer as a fraction. (Note to type the fraction $\frac34$ , type 3/4)

$k\left(h(\var{n})\right)=$ $h\left(k(\var{n})\right)=$ Unnamed gap

Advice

Part a)

We have

$\begin{align}k\left(h(\var{n})\right)&=k\left(\simplify[!collectNumbers]{({a}*{n}+{b})/({c}*{n}+{d})}\right)\\&=k(\var[fractionNumbers]{eval(f_x,["x":n])})\\&= \var[fractionNumbers]{comb_n}\end{align}$

We have

$\begin{align}h\left(k(\var{n})\right)&=h\left(\simplify[!collectNumbers]{{l}*{n}+{m}}\right)\\&=h(\var[fractionNumbers]{eval(g_x,["x":n])})\\&= \var[fractionNumbers]{comb_n}\end{align}$

Part b)

The domain of a function is the set of possible inputs. The function $h(x)$ will not produce an output if it's denominator is $0$ , that is if $x=\simplify[fractionNumbers]{-{d/c}}$ . Hence the domain of $h(x)$ will be all real numbers except $x=\simplify[fractionNumbers]{-{rational(d/c)}}$ .

Part c)

We require

$\begin{align}h\left( k(x)\right)&=h\left(\simplify{{l}x+{m}}\right)\\&=\frac{\simplify{{a}({l}x+{m})+{b}}}{\simplify{{c}({l}x+{m})+{d}}}\\&=\frac{\simplify[expandBrackets,collectNumbers,cancelTerms]{{a*l}x+{a*m+b}}}{\simplify[expandBrackets,collectNumbers,cancelTerms]{{c*l}x+{c*m+d}}}\end{align}$

We require

$\begin{align}k\left( h(x)\right)&=k\left(\frac{\simplify{{a}x+{b}}}{\simplify{{c}x+{d}}}\right)\\&=\simplify{{l}*({a}x+{b})/({c}x+{d})+{m}}\\&=\frac{\simplify{{l*a}x+{l*b}+{m*c}x+{m*d}}}{\simplify{{c}x+{d}}}\end{align}$

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
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Choose one from a list
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Gap-fill
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Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exams:

SCC Class Test 2 by Hanh Vo in SCC PrelimMaths.
SCC Class Test 2 by Hanh Vo in SCC PrelimMaths.
Don's copy of Class Test 2 by Don Shearman in MfEP Progress Quizzes.
Class Test 2 by Don Shearman in MfEP Progress Quizzes.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Don Shearman 11 months, 2 weeks ago

Don Shearman 3 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `expression`

Parts

Gap-fill

Part a)

Part b)

Part c)

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Error

Functions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Don Shearman 11 months, 2 weeks ago

Don Shearman 3 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: expression

Parts

Gap-fill

Part a)

Part b)

Part c)

Generated value: `expression`