If f(x) = x2, which of the following describes the graph of f(x - 1)?
the graph of f(x - 1) is a horizontal shift of f(x) = x2 one unit to the right.
the graph of f(x - 1) is a vertical shift of f(x) = x2 one unit down.
the graph of f(x - 1) is a vertical shift of f(x) = x2 one unit up.
the graph of f(x - 1) is a horizontal shift of f(x) = x2 one unit to the left.

The correct answer is:

The graph of f(x - 1) is a horizontal shift of f(x) = x^2 one unit to the right.

We are given a parent function f(x) as:

Now we have to find what is the behavior of the graph of the transformed function:

Now we know that the transformation of the type:

with respect to the parent function f(x) is a shift either to the right or to the left i.e. a horizontal shift depending upon the sign of the constant 'a'.

If a>0 then the shift is to the left by 'a' units.

and if a<0 then the shift of he function is to the right by 'a' units.

Hence, here f(x-1) is a shift of the function f(x) to the right by '1' unit.

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb