What is Sasha's monthly gross if her annual salary is $41,100?_
1 answer:
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We start with the parent function
The first child function would be
We have multiplied the input of the function by a constant: we have
This kind of transformation result in a horizontal stretch/compression. If the multiplier is greater than 1, we have a compression. So, this first child causes a horizontal compression with compression rate 2.
The second child function would be
We added 6 to the input of the function: we have
This kind of transformation result in a horizontal translation. If the constant added is positive, we translate to the left. So, this second child causes a translation 6 units to the left.
The third child function would be
We changed the sign of the previous function (i.e. we multiplied it by -1): we have
This kind of transformation result in a vertical stretch/compression. If the multiplier is greater than 1 we have a stretch, if it's between 0 and 1 we have compression. If it's negative, we reflect across the x axis, and then apply the stretch/compression. In this case, the multiplier is -1, so we only reflect across the x axis.
The fourth child function would be
We added 3 to previous function: we have
This kind of transformation result in a vertical translation. If the constant added is positive, we translate upwards. So, this last child causes a translation 3 units up.
Recap
Starting from the parent function , we have to:
- Compress the graph horizontall, with scale factor 2;
- Translate the graph 6 units to the left;
- Reflect the graph across the x axis;
- Translate the graph 3 units up
Note that the order is important!
Answer:
The taylor's series for f(x) = ln x centered at c = 1 is:
Step-by-step explanation:
The calculations are handwritten for clarity and easiness of expression.
However, the following steps were taken in arriving at the result:
1) Write the general formula for Taylor series expansion
2) Since the function is centered at c = 1, find f(1)
3) Get up to four derivatives of f(x) (i.e. f'(x), f''(x), f'''(x), )
4) Find the values of these derivatives at x =1
5) Substitute all these values into the general Taylor series formula
6) The resulting equation is the Taylor series
Here is your graph of the system. Where they cross is the answer, which is -4. Pretty much you have to graph each equation and where they meet is the answer.
