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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: gmx on March 22, 2010, 10:23:49 pm

Title: maths function how to sketch?
Post by: gmx on March 22, 2010, 10:23:49 pm: Hello internet,

"Sketch the graph of the functions, showing intercepts and asymptotes, and stating the domain and range of each one :f(x) = 1 − 3^(2 − x)"

Would you be able to show me this step by step with an explanation of what you are doing?

Thank you
Title: Re: maths function how to sketch?
Post by: TrueTears on March 23, 2010, 01:10:15 am: f(x) = -31 - x

this is a linear graph with y axis intercept at y = -31
Title: Re: maths function how to sketch?
Post by: moekamo on March 23, 2010, 04:16:53 am: simplify to make a bit easier: $f(x)=1-3^{2-x}=1-3^2 \cdot 3^{-x}=1-9\cdot 3^{-x}$

apply transformations: reflection in x & y axis, dilation by 9 from x axis, translation one unit up

plug in a few points, eg $f(0)=-8$ , asymptote at y=1(because of vertical translation by one),

find x int:
$0=1-3^{2-x}$
$\implies 1=3^{2-x}$
$\implies 2-x=0, x=2$

so x int at (2,0)

also make sure ur graph is smooth and axes are labelled, not like my sketch!

domain: $x\in \mathbb{R}$
range: $y\in (-\infty , 1)$