Question

3. Which translation rule describes the translation that is 6 units to the left and 5 units up? (1 point)

Answer 1

3. Translation that is 6 units to the left and 5 units up translate the point (x,y) into the point (x-6,y+5).

Example: if you translate the origin (0,0) 6 units to the left and 5 units up, then you obtain point (-6,5).

Answer 3: correct choice is D.

4. A reflection across the y­-axis changes the x-values into opposite and y-values remain the same. Then the rule is (x,y)→(-x,y).

Example: if you reflect the point (2,3) across the y-axis, then you get the point (-2,3).

Answer 4: correct choice is B.

Answer 2

Question 1:

 For this case suppose we have a function f (x).
 We then have the following transformations:
 Horizontal displacements:
 Suppose k> 0
 To move the graph k units to the left, we must graph f (x + k)
 Vertical displacements:
 Suppose k> 0
 To move the graph k units up we must graph f (x) + k
 Therefore, using the definitions, the rule that describes 6 units to the left and 5 units up is:
 (x, y) (x + 6, y + 5)
 Answer:
 C. (x, y) (x + 6, y + 5)

 Question 2:

 For this case suppose we have a function f (x).
 We then have the following transformation:
 Reflections:
 To graph y = f (-x), reflect the graph of y = f (x) on the y-axis. (Horizontal reflection)
 Therefore, using the definition, the rule that describes the transformation is:
 (x, y) → (-x, y)
 Answer:
 B. (x, y) → (-x, y)