3. Functions

Graph each piecewise-defined function.

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-2, -6) and (3, −4)

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=-|x+4|

Graph each equation. ƒ(x) = x

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. x²+y²+2x-6y+14=0

Determine whether each relation defines a function, and give the domain and range.

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. center (5, -4), radius 7

Fill in the blank(s) to correctly complete each sentence. The equation y = 4x - 6 defines a function with independent variable______ and dependent variable ________ .

Determine whether each relation defines a function, and give the domain and range.

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. x²+y²+4x-8y+32=0

Find ƒ+g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

Determine the intervals of the domain over which each function is continuous.

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x²? What is its domain?

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. 2x+3y=5

For each function graphed, give the minimum and maximum values of ƒ(x) and the x-values at which they occur.