# Determine the transformations of the function f(x) to get the function g(x) =1/2f(5(x−3))−12 (The transformations happen in c, b, a, d order)

Question
Performing transformations
Determine the transformations of the function f(x) to get the function $$g(x) =1/2f(5(x−3))−12$$ (The transformations happen in c, b, a, d order)

2020-11-09
Given:
A function f(x) is transformed to get a function g(x).
$$=>g(x)=1/2f(5(x-3))-12$$
sequence of the transformations to transform f(x) into g(x) is given by:
$$=>$$ Vertical compression by a scale factor of $$1/2$$
$$=>$$ Horizontal compression by a scale factor of 5
$$=>$$ Horizontal translation of 3 units to the right
$$=>$$ Vertical translation of 12 units down

### Relevant Questions

Your friend attempted to describe the transformations applied to the graph of $$y=sinx$$ to give the equation $$f(x)=1/2sin(-1/3(x+30))+1$$.
They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.
a) f(x) has been reflected vertically.
b) f(x) has been stretched vertically by a factor of 2.
c) f(x) has been stretched horizontally by a factor of 3.
d) f(x) has a phase shift left 30 degrees.
e) f(x) has been translated up 1 unit.
Let T $$\displaystyle{P}_{{2}}\rightarrow\mathbb{R}^{{3}}$$ be a transformation given by
$$\displaystyle{T}{\left({f{{\left({x}\right)}}}\right)}={\left[\begin{array}{c} {f{{\left({0}\right)}}}\\{f{{\left({1}\right)}}}\\{2}{f{{\left({1}\right)}}}\end{array}\right]}$$
(a)Then show that T is a linear transformation.
(b)Find and describe the kernel(null space) of T i.e Ker(T) and range of T.
(c)Show that T is one-to-one.
Starting with the function $$f(x) = e^x$$, create a new function by performing the following transformations.
i. First shift the graph of f (x) to the left by two units.
$$f_1 (x) =$$?
ii. Then compress your result by a factor of $$1/7$$
$$f_2 (x) =$$ ?
iii. Next, reflect it across the x-axis.
$$f_3 (x) =$$ ?
iv. And finally shift it up by eight units to create g (x).
g (x) =?
List a sequence of transformations, in words, to convert the graph of $$f(x)=x^2$$ into the graph of $$g(x)=-6(x-2)^2+5$$.
Create a new function in the form $$y = a(x-h)^2 + k$$ by performing the following transformations on $$f (x) = x^2$$.
Give the coordinates of the vertex for the new parabola.
g(x) is f (x) shifted right 7 units, stretched by a factor of 9, and then shifted down by 3 units. g(x) = ?
Coordinates of the vertex for the new parabola are:
x=?
y=?
The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P $$(A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).$$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
Given $$f(x)=x^2$$, after performing following transformations shift upwards 18 units and shift 89 units to the right, the new function g(x)=?
Given $$f(x)=x^2$$ after performing the following transformations shifted upwards 90 units and shifted 87 units to right, the new function g(x)=?
Given $$f(x)=x^2$$, after performing the following transformations: shift upward 52 units and shift 23 units to the right, write the new function