3. Functions

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

Graph each piecewise-defined function.

Give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x + 1)² + y² = 25

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (2, 3) and (14, 8)

Find the domain of each function. g(x) = 3/(x²-2x-15)

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y = -x³

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. x² + (y − 1)² = 1

Find the domain of each function. f(x) = 1/(x²+1) - 1/(x²-1)

Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. |x| = |y|

Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. ƒ(-3)

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. center (2, 0), radius 6

Let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. (fog) (0)

Find the domain of each function. f(x) = 1/[4/(x - 1) - 2]

Graph each function. Give the domain and range. ƒ(x)=-[[x]]