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.

PA = ST, PB = SU, AB = TU ⇒ ∠P = ∠Q

Step-by-step explanation:

Point S is drawn to mimic point P.

The length of PA is measured and copied to point S so PA = ST.

The length of PB is measured and copied to point U so PB = SU.

Now we know that AB = SU.

Since all of the sides are congruent (if we were to draw a triangle), we can state that the triangles are congruent by Side-Side-Side Congruency Theorem.  Thus, ∠P ≡ ∠S  by CPCTC Theorem.