Make a table of values for f(x) after the given translation 3 units up

In this case, we do not have the table, so i will answer in a general way:

First, let's describe the transformation.

Vertical shift.

If we have a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

This will move the graph of f(x) up or down a distance of N units.

if N is positive, then the shift is upwards

if N is negative, then the shift is downwards.

Then a shift of 3 units up, is written as:

g(x) = f(x) + 3

This would be translated to the table in the next way:

You need to add 3 to all the values of y (or f(x)) in the table:

So if for example, the original table was:

x            f(x)

0             5

1              7

2             10

3              15

The table of the transformation will be:

x              g(x)

0              5 + 3 = 8

1               7 + 3 = 10

2              10 + 3 = 13

3               15 + 3 = 18

4

step-by-step explanation: