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)

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.

Multiply the number of days (x) by the amount per day (80) to get 80x.

She is driving 150 miles at 0.10 per mile so multiply to get the mileage cost: 150 x 0.10 = 15

Add this to the daily amount:

80x+15

She can spend up to 300, so less than or equal to 300:

80x +15 <=300