3. Functions

Exercises 103–105 will help you prepare for the material covered in the next section. Let (x1, y₁) = (7, 2) and (x2, y2) = (1, −1). Find √[(x2 − x1)² + (y2 − y₁)²]. Express the - answer in simplified radical form.

Fill in the blank(s) to correctly complete each sentence. The circle with center (3, 6) and radius 4 has equation _________.

In Exercises 109–111, give the center and radius of each circle. x^2 + y^2 - 4x + 2y - 4 = 0

In Exercises 107–108, write the standard form of the equation of the circle with the given center and radius. Center (-2. 4), r = 6

In Exercises 105–106, find the midpoint of each line segment with the given endpoints. (2, 6) and (-12, 4)

Find the given distances between points P, Q, R, and S on a number line, with coordi-nates -4, -1, 8, and 12, respectively. d(P, Q)

Find the given distances between points P, Q, R, and S on a number line, with coordi-nates -4, -1, 8, and 12, respectively. d(Q,R)

Fill in the blank(s) to correctly complete each sentence. The circle with equation x^2+y^2=49 has center with coordinates________ and radius equal to__________ .

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (0, 0), radius 6

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (2, 0), radius 6

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (0, 4), radius 4

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (5, -4), radius 7

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (-2, 5), radius 4

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (√2, √2), radius √2

Use each graph to determine an equation of the circle in (a) center-radius form and (b) general form.