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wel
3 years ago
7

Describe the transformation of the graph y = (x + 3)2 – 4 from the parent function y = x².

Mathematics
1 answer:
Mazyrski [523]3 years ago
6 0
The answer is A.  Left 3 and Down 4

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-Dominant- [34]

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C

Step-by-step explanation:

An approximation of an integral is given by:

\displaystyle \int_a^bf(x)\, dx\approx \sum_{k=1}^nf(x_k)\Delta x\text{ where } \Delta x=\frac{b-a}{n}

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\displaystyle \Delta x=\frac{8-2}{n}=\frac{6}{n}

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And the right endpoint is modeled with:

x_k=a+\Delta xk

Since we are using a Left Riemann Sum, we will use the first equation.

Our function is:

f(x)=\cos(x^2)

Therefore:

f(x_k)=\cos((a+\Delta x(k-1))^2)

By substitution:

\displaystyle f(x_k)=\cos((2+\frac{6}{n}(k-1))^2)

Putting it all together:

\displaystyle \int_2^8\cos(x^2)\, dx\approx \sum_{k=1}^{n}\Big(\cos((2+\frac{6}{n}(k-1))^2)\Big)\frac{6}{n}

Thus, our answer is C.

*Note: Not sure why they placed the exponent outside the cosine. Perhaps it was a typo. But C will most likely be the correct answer regardless.

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