1.

If an algebraic expression defines a function without reference to its domain, then we assume that the domain is the set of all real numbers for which the expression is applicable. Find the domain and range of the following functions.

1. -2 x

2. 3 x + 2

3. x ²

4. -x ³ + 1

5. -x ² + 2

6. sin x

7. ( x + l) ^1/2

8. (1 - x ²) ^-2

2.

Is the rule or function that sends a point ( x, y) to ( x ², y) a geometric transformation? Explain your answer.

3.

Is the rule or function that sends a point ( x, y) to ( x, y ³) a geometric transformation? Explain your answer.

4.

Let ? _l and ? _m be reflections of a circle in a pair of perpendicular diameters l and m. Show that ? _m ? _l is equivalent to a reflection of the circle in its center.

5.

Find the inverse of each of the following functions,

1. x' = f( x) = -x

2. x' = f( x) = 2 x + 1

3. x' = f( x) = 3 x - 5

4. x' = f( x) = -x + 1

5. x' = f( x) = x ³

6.

Decide whether or not...