Urgent! Can someone please answer? Thanks

Question

Which transformation represents the following rule? (x,y) (x,y-b)

A. Horizontal translation to the right

B. Horizontal translation to the left

C. Vertical translation down

D. Vertical translation up

Answer 1

Hi Juliana,

your question is about (x,y) & (x,y-b) that what the new position for point (x,y-b) is

first, when changes occurred on y always translation is vertical

second, if b is a positive number, point such as (x,y) vertically goes down as a b units

Example: point A is (2,3) and b = 5 then we have new point such as (2, 3-5) will be (2, -2)

It means point A 5 units goes down

Third, if b is negative number, point such as (x,y) vertically goes up as a b units

Example: point A is (2,3) and b = -5 then we have new point such as (2, 3-(-5)) will be (2, 8)

It means point A, 5 units goes up

I suggest, you graph both examples on the coordinate plane then you figure out much better.

I hope it is useful,

Minoo

Answer 2

Which transformation represents the following rule? (x,y) (x,y-b)

Vertical translations (up or down) occur to the y values, positive values translate the graph up, negative translate it down.

In this case, y - b will translate the graph down by b units.

Here are helpful rules for functions to commit to memory:

f(x) +/- d, (x,y) →(x, y +/-d) vertical translations up/down d units

f(x +/- c), (x,y) →(x +/- c, y) horizontal translation left(+)/right(-) c units

-f(x), (x,y) → (x, -y) reflection over the x-axis

f(-x), (x,y) → (-x,y) reflection over the y-axis

af(x), (x,y) →(x, (a)y) vertical stretch/compression (stretch |a|>1,compression 0<|a|<1 )

f(ax), (x,y)→(x/a, y) horizontal compression/stretch (compression |a|>1, stretch 0<|a|<1 )