In this given graph, f(x) is a polynomial modeling the Pi-guy, the math superhero, flying around. Write an equation in terms of the parent function with each transformation. No need to be specific just write in terms of f(x) 1. What is being asked in the problem and what does it mean?

2. What plan am I going to try?

3. Create an outline or map to organize your answer

4. How can you check it ?

The given transformation are;

1) Parent function = f(x)

2) Transformation A = f(x + 5)

3) Transformation B = f(x) + 3

Step-by-step explanation:

1. The question being asked in the problem is the representation of the transformation of the given figure which is a function (the curved line that runs through the hands of Pi-guy in the drawing) in functional notation using f(x) to represent the function

2. Try using changes along the x axis as changes in the independent variable, x, in the function f(x) as follows;

Initial position of the parent function = f(x)

Transformation A, which is a translation, 5 units to the right along the x axis = f(x + 5)

Transformation along the y-axis where x = 0, as addition or subtraction to the parent function

Therefore;

Transformation B, which is a translation, 3 units to the up along the y-axis with x at 0 = f(x) + 3

3. The outline of the answers can be presented as follows

The given transformation are;

1) Parent function = f(x)

2) Transformation A = f(x + 5)

3) Transformation B = f(x) + 3

4. The above expression can be checked by considering the curve of the function as a figure and performing the given translations on all points on the figure

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).