Question

Please help 15 points

How are the functions y = x and y = x - 3 related? How are their graphs related?

A. Each output for y = x - 3 is 3 more than the corresponding output for y=x.
The graph of y = x - 3 is the graph of y = x translated down 3 units.

B. Each output for y = x-3 is 3 more than the corresponding output for y = x.
The graph of y = x - 3 is the graph of y = x translated up 3 units.

C. Each output for y = x - 3 is 3 less than the corresponding output for y = x.
The graph of y = x - 3 is the graph of y = x translated down 3 units.

D. Each output for y = x-3 is 3 less than the corresponding output for y=x.
The graph of y = x - 3 is the graph of y = x translated up 3 units.

Answer 1

Answer: C

Step-by-step explanation: Because The graph of y = x - 3 is a translation of y = x by three units down, every x-coordinates on the equation y = x is to be decreased by 3 units. Also, It is y=x-3 so the answers B and D are eliminated since they say it is translated upwards. Also, since it is x-3 it is less than the output of y=x, so A is eliminated. The only option left is C.

Answer 2

The correct option is C.

Explanation:

The given functions are

`y=x` ... (1)

`y=x-3` .... (2)

The translation is defined as

`y=x+b` .... (3)

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (2) and (3) we get b=-3. It means the graph of y = x translated down 3 units to get the graph of y = x - 3.

Output of first function is equal to x and output of second function is x-3. It means each output for y = x - 3 is 3 less than the corresponding output for y = x.

Therefore the correct option is C.