Question

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)

Answer 1

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)

Answer 2

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.