Question

Describe how to transform the graph of f into the graph of g.

f(x) = square root of quantity x minus eight. and g(x) = square root of quantity x plus four.

Answer 1

g(x) is obtained by shifting the graph of f(x) 12 units in the left.

Explanation:

we are given the function f(x) and g(x) as:

`f(x)=√(x-8)` and
`g(x)=√(x+4)` or we can also say that
`g(x)=f(x+12)`.

so any function g(x)=f(x+h) is formed by shifting the function either to the right or to the left of the graph depending on whether this 'h' is positive or negative.

if h>0 then the shift will be towards the left and if this h<0 then the shift will be towards the right by 'h' units.

here h=12>0

Hence, g(x) is obtained by shifting the graph of f(x) 12 units in the left.

Answer 2

f(x) = √(x - 8)
g(x) = √(x + 4)

The graph of g is obtained by shifting the graph of f 12 units to the left.