3. Functions

Exercises 103–105 will help you prepare for the material covered in the next section. Use a rectangular coordinate system to graph the circle with center (1, -1) and radius 1.

Graph each equation.

$\text{ƒ}\left(x\right)=3$

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

Find fg and determine the domain for each function. f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. x=y⁴

Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. ƒ(-7/3)

Find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2).

f(x) = 2x-3, g(x) = (x+3)/2

Find the domain of each function. f(x) = 1/√(x - 3)

Find a. (fog) (x) b. the domain of f o g.

f(x) = √x, g(x) = x − 2

Graph each function.

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (3√3, √5) and (−√3, 4√5)

Determine whether each relation defines a function. {(8,0),(5,7),(9,3),(3,8)}

Write the standard form of the equation of the circle with the given center and radius. Center (−3, −1), r = √3

Determine whether each function is even, odd, or neither. ƒ(x)=x⁴+4/x²

Graph each piecewise-defined function.