3. Functions

Exercises 103–105 will help you prepare for the material covered in the next section. Solve by completing the square: y² – 6y — 4 = 0.

Find the value of the function for the given value of x. ƒ(x)=2-[[-x]], for x=3.7

Determine whether each statement is true or false. If false, explain why. The midpoint of the segment joining (0, 0) and (4, 4) is 2.

Consider the following nonlinear system. Work Exercises 75 –80 in order.

y = | x - 1 |

y = x² - 4

Use the definition of absolute value to write y = | x - 1 | as a piecewise-defined function.

Find f/g and determine the domain for each function. f(x) = √x, g(x) = x − 4

Give a rule for each piecewise-defined function. Also give the domain and range.

Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. g(10)

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

Graph each function.

$\text{ƒ}\left(x\right)=-\mid x\mid$

Use a graphing calculator to graph each equation in the standard viewing window. -2x + 5y = 10

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

Find the domain and range of the following graph (write your answer using interval notation).

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 for the first ounce?