Question

5. The graph of g(x) results when the graph of f(x) = -|x| is shifted 3 units to the left.

Which is the equation of g(x)?

Answer 1

to shift left by 3 units, simply replace x wid 'x+3'

Answer 2

So would it be this? g(x) = -|x + 3|

Answer 3

yes !

Answer 4

In general, if you take a function and replace the "x" with (x-h), the graph of the new function is shifted to the right by h units. (Note the "-"!) If the "x" is replaced by (x+h) then think of it as (x - (-h)). Then the shift is -h units to the right. And since left is the opposite of right, -h units to the right is the same as h units to the left. Similarly if the y is replaced by (y-k) the graph is shifted up k units and if the y is replaced by (y+k) the graph is shifted down k units.

With function notation the "y" is f(x) (or g(x) or h(x) or ...).

So let's see what we can do to f(x) = |x| to turn it into |x+3|+5:
If we replace the x with (x+3), which shifts the graph to the left by 3 units, we get


f(x) = |x+3|
If we replace f(x) by f(x)-5, shifting the graph up 5 units, we get
f(x) - 5 = |x+3|
Adding 5 to both sides we get:
f(x) = |x+3|+5
which is g(x)! So the answer is (1) 3 left, 5 up