Triangle abc looks like a right triangle show

Question

Let f(x) = x² and g(x) = x - 2

a. What is f o g(x)?

b. What is g o f(x)?

c. What is f ? f(x) ?

d. What is g'(x) = [ g(x+h) - g(h)] / h ?

e. What is f '(x) = [ f(x+h) - f(x)] / h?

Plot the following points. You can use the www.desmos.com/calculator 

a. A(8,19), B(13,-5), C(-7,-9)

b. What is the length of line segment AB?

c. What is the mid-point of line segment AB?

d. What is the length of line segment BC?

e. What is the mid-point of line segment BC?

f. What is the length of line segment CA?

g. What is the mid-point of line segment CA?

h. Triangle ABC looks like a right triangle. Show mathematically whether it actually is or is not a right triangle.

Write the equations of the following.

a. A line with slope 3 and y-intercept 5.

b. A circle of radius 4 centered on the point (5,-3)

c. A line with slope -3 which passes through the point (-2,1)

What type of symmetry do each of the following equations have? (even, odd, or neither). If there is symmetry, what is the equation of the axis of symmetry? Plot each of the equations and the axis of symmetry (or to show that it has no axis of symmetry) to verify your answer.

a. y = (x - 5)(x + 5)

b. y = x³ - x² -2x + 1

c. y = x³ - x

d. y = x² -2x + 6

e. y = |2x + 1|

Given the following function : y = f(x) = 3x + 2

How can the following shifts and scale changes to get

a. y₁ = f(x) -2

b. y₂ = f(x-2)

c. y₃ = 2f(x)

d. y₄ = f(3x)

e. y₅ = f(x) * f(x)