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secondary 3 | E Maths
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Damien Tan
Damien Tan

secondary 3 chevron_right E Maths chevron_right Singapore

Hi, this is the Graph topic for Emath. I do not understand why the asymptote affect the value of b. In this case, why y = b = 1

Date Posted: 5 years ago
Views: 264
J
J
5 years ago
Because b is the value of the asymptote.


This graph is of the type y = a^x + b.
The y-value is always positive as shown in the graph (asymptote is above x-axis, so the value of y can never reach it, let alone below 0)

Realise that in this graph, a^x is always positive for all real values of x. This means a is positive. Try it on a calculator using different values of x and (negative and positive) and a (positive).

So, since y = a^x + b, and a^x is always positive,

y is always = b + (something positive).
This also means y always > b for any real value of x. Value of y will never reach b.

In this graph,the asymptote is the line y = 1. So value of y in the graph is always > 1 and never reaches 1.

From this and the above deduction, you'll realise b = 1.
Damien Tan
Damien Tan
5 years ago
Understood. Thank you :)

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Wong Jing Kuan
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Jonathan Goh Shi Nam
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there is an asymptote at y=1. this means that the graph is shifted up by 1 unit and hence the value of b must be 1. For equations y = f(x) +c, c is the number of units that the graph is translated/shifted in the direction of the y-axis.