Given the function hx Squareroot x perform the transformati

Given the function h(x) = Squareroot x, perform the transformations (a), (b), and (c) below and graph the final result (make sure to write your resulting transformation in every step). Use the grid provided in Figure 3 for your convenience. Shift the original function up 1 unit. Write down your expression for the new function. Reflect the result of part a) about the x-axis. Write down your expression for the new function. Reflect the result of part b) about the y-axis. Write down your final expression.

Solution

If the parent function is y = f(x), then the translation of the function horizontally to the left or right (in the x-direction) is given by the function f(x – h).

if h > 0, the graph translates to the right.
if h < 0, the graph translates to the left.

If the parent function is y = f(x), then the translation of the function vertically up or down (in the y-direction) is given by the function f(x) + k.

if k > 0, the graph translates upward.
if k < 0, the graph translates downward.

b) y=sqrt (x+1)

c) y= sqrt (x)+1