1. The function y = √f(x) is the square root of the function y = f(x)
Ex. Given f(x) = 3 - 2x, graph f(x) and
Invariant points occur when f(x) = 0 and f(x) = 1
because at these values √f(x) = f(x)

2. Characteristics:
below f(x)

3. Ex. Given the graphs of f(x) , sketch √f(x) .
Locate invariant points
Step 2: Draw the part of the graph between the invariant
points above f(x) and g(x)
Locate other key points at perfect squares and
draw them in
Step 4: Sketch a smooth curve between the points.
(They will be below f(x) and g(x))
Remember: Nothing should be below the x-axis!!

4. Ex. Given the graphs of g(x), sketch √g(x).

5. Ex. Given the graphs of h(x), sketch √h(x).

6. Ex. Given the graphs of p(x) sketch √p(x)