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# Polynomials, Please Explain When Solving

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Apr 21, 2021

#1
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a) In order to plot g(x) we translate the endpoints of f(x)  as follows :-

$$(-4,4)$$ in f(x) ⇔ $$(-13,2)$$ in g(x)

$$(0,2)$$ in f(x) ⇔ $$(-1,1)$$ in g(x)

$$(-1,0)$$ in f(x) ⇔ $$(-4,0)$$ in g(x)

$$(4,-4)$$ in f(x) ⇔ $$(11,-2)$$ in g(x)

∴ The graph of g(x) is plotted below - ________________________________________________________________________________________________________

b) Each point $$(a,b)$$ in  f(x) becomes $$(3a-1,{b \over 2})$$ in g(x).

Now, that implies a horizontal stretch by a factor of 3 and a horizontal shift by 1 unit left for a.

So, that gives us $$f({1 \over 3}.(x+1))$$

As for b, the graph shrinks vertically by a factor of $$1\over 2$$

So that gives $${1\ \over 2}f({1 \over 3}.(x+1))$$

So that completes,

$$g(x) = {1 \over 2}f({x+1 \over 3})$$

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c) In order to get the graph $$y=g(x)$$, the original graph can be stretched horizontally  by a factor of 3, then shrunk vertically by a factor of 1/2 and shifted left by 1 unit.

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~ It's a pleasure! :)

Apr 30, 2021