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lesya [120]
3 years ago
6

I am really confused about this question for math.. any help would be really appreciated:

Mathematics
1 answer:
Elina [12.6K]3 years ago
6 0

y= (\frac 1 4 )^x

A reflection about the x axis, about y=0, is the mapping (x',y')=(x,-y) so

y'= -y = - (\frac 1 4)^{x'}

A dilation of 2 is the mapping (x'',y'')=(2x', 2y')

So

x'=x''/2, y'=y''/2

y''/2= - (\frac 1 4)^{x''/2}

y'' =  - 2((\frac 1 4)^{1/2})^{x''}

y''= - 2(\frac 1 2)^{x''}

We can rewrite that without the primes and combine the powers of 2.

y =  - 2^{1-x}

Let's graph these and see if we're close,

Plot y= (1/4)^x, y= - (1/4)^{x}, y = - 2^{1-x}

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If r(X)=2-x^2 and w(X)=X-2, what is the range of (w*r)(X)
slega [8]
The given function are
r(x) = 2 - x²    and     w(x) = x - 2
<span>(w*r)(x) can be obtained by multiplying the both function together
</span>
So, <span>(w*r)(x) = w(x) * r(x) = (x-2)*(2-x²)</span>
<span>(w*r)(x) = x (2-x²) - 2(2-x²)</span>
            = 2x - x³ - 4 + 2x²

∴ <span>(w*r)(x) = -x³ + 2x² + 2x - 4
</span>

<span>It is a polynomial function with a domain equal to R
</span>
The range of <span>(w*r)(x) can be obtained by graphing the function
</span>
To graph (w*r)(x), we need to make a table between x and (w*r)(x)

See the attached figure which represents the table and the graph of <span>(w*r)(x)
</span>

As shown in the graph the range of <span>(w*r)(x) is (-∞,∞)
</span>

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