3. Functions

Graph each piecewise-defined function.

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

Graph each function. ƒ(x) = 2∛(x+1)-2

For each function graphed, give the minimum and maximum values of ƒ(x) and the x-values at which they occur.

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

In Exercises 77–92, use the graph to determine a.the x-intercepts, if any; b. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. (x − 2)²+(y+3)² = 4, y = x - 3

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. x²+y²+4x+4y+8=0

Find the midpoint of each line segment with the given endpoints. (-3, -4) and (6, −8)

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

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

Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. ƒ(x+2)

Find the domain of each function. $f\left(x\right)=x/(x^2+4x-21)$

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)

Find f/g and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)