3. which translation rule describes the translation that is 6 units to the left and 5 units up? (1 point)
a. (x, y) (x + 6, y – 5)
b. (x, y) (x – 6, y – 5)
c. (x, y) (x + 6, y + 5)
d. (x, y) (x – 6, y + 5)
4. which rule describes the transformation that is a reflection across the y­axis? (1 point)
a. (x, y) → (x, –y)
b. (x, y) → (–x, y)
c. (x, y) → (–x, –y)
d. (x, y) → (y, x)

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)
 
 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)
 
 B. (x, y) → (-x, y)