3. Functions

Determine whether each relation defines a function, and give the domain and range. {(1,1),(1,-1),(0,0),(2,4),(2,-4)}

Give the center and radius of the circle represented by each equation. x²+y²-4x+12y=-4

Find a. (fog) (x) b. (go f) (x) f(x) = x²+2, g(x) = x² – 2

Determine whether each equation defines y as a function of x. x = (1/3)(y²)

Choose the correct answer: For function ƒ, the notation ƒ(3) means

A. the variable f times 3, or 3f.

B. the value of the dependent variable when the independent variable is 3.

C. the value of the independent variable when the dependent variable is 3.

D. f equals 3.

Graph each piecewise-defined function.

Determine whether the three points are the vertices of a right triangle. See Example 3.

$(-2,-8),(0,-4),(-4,-7)$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+8x-2y-8=0

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² - 6y -7=0

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² − x + 2y + 1 = 0

Find ƒ+g and determine the domain for each function.

f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)

Find ƒ+g, ƒ- g, ƒg and ƒ/g. Determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. P(3, -1), Q(-4, 5)

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. $5y^2+5x^2=30$

Find ƒ/g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1