3. Functions

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid-point M of line segment PQ. P(8,2), Q(3,5)

Give the center and radius of the circle represented by each equation. x²+y²+6x+8y+9=0

Find the midpoint of each line segment with the given endpoints. (-7/2, 3/2) and (-5/2, -11/2)

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² - 2x + y² – 15 = 0

Determine the largest open intervals of the domain over which each function is (c) constant. See Example 9.

Solve each problem. See Example 4. Suppose that the cost of mailing a letter weighing x ounces, where x>0, is ƒ(x)=55-15[[1-x]]cents. What is the cost of mailing a 2.6-ounce letter?

Determine whether the three points are collinear. (0, 9),(-3, -7),(2, 19)

Find the value of the function for the given value of x.

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-1/4, -1/7) and (3/4, 6/7)

Find the domain of each function. g(x) = 2/(x+5)

In Exercises 59-64, 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. g (f[h (1)])

Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Example 5(b).

midpoint $(5,8)$, endpoint $(13,10)$

Find a. (fog) (2) b. (go f) (2) f(x)=4x-3, g(x) = 5x² - 2

Determine whether each relation defines y as a function of x. Give the domain and range. y=2/(x-3)

Write the standard form of the equation of the circle with the given center and radius. Center (0, 0), r = 7