Find and simplify the difference quotient - vertical line

Question

Problem 1:

Express the following sets of numbers using interval notation:

{x\x < - 2 or x > 0}

Problem 2:

Find the midpoint of the line segment connecting P(-2; 5) and Q(4;

Problem 3:

Determined whether or not (-1, 0) is on the graph x² + y³ = 1.

Problem 4:

Find the x- and y- intercepts (if any) of the graph of (x - 2)² + y²

Problem 5:

Use the Vertical Line Test to determine if the following relation describes y as a function of x.

Problem 6:

What are the domain and range of the following function:

f (x) = Vx³ - 8

Problem 7:

What are the domain and range of the following function:
f (x) = V7 - x

Problem 8:

The area A enclosed by a square, in square inches, is a function of the length of one of its sides x, when measured in inches. This relation is expressed by the formula A(x) = x2 for x > 0. Find A(2) and solve A(x) = 49. Interpret your answers to each. Why is x restricted to x > 0?

Problem 9:

Let f (x) = 6x² - x and g(x) = 4 - X. Find (f + g)(-1)

Problem 10:

Find and simplify the difference quotient for the following function:

f (x) = x² - 2x + 3