5.3 Graphing Radical Functions

Radical Functions A radical function contains a radical expression with the independent variable in the radicand. When the radical is a square root, the function is called a square root function. When the radical is a cube root, the function is called a cube root function.

Square Root Functions The radicand of a square root must be nonnegative. Domain: Range: Domain: Range: h

Cube Root Functions The domain and range of cube root functions are all real numbers. Domain: all real numbers Range: all real numbers Domain: all real numbers Range: all real numbers h

Example 1: Solution: 1. Make a table of values 2. Sketch the graph 4 8 12 16 y 1 1.4 1.73 2 2. Sketch the graph 3. Domain and Range

Transformation You can transform graphs of radical functions in the same way you transformed graphs of functions previously. Transformation f(x) notation Example Horizontal Translation - shifts graph left/right f(x – h) Vertical Translation - shifts graph up/down f(x) + k f(-x) -f(x) Reflection - graph flips over x or y axis Horizontal Stretch/Shrink graph stretches away from or shrinks toward y axis f(ax) Vertical Stretch/Shrink graph stretches away from or shrinks toward x axis a • f(x)

Example 2: Solution: h = 3: shift three units right k = 4: shift four units up

Example 3: Solution Step 1 Understand the Problem Step 3 Solve the Problem Step 4 Look Back Step 2 Make a Plan

:D Example 4: Solution:

Example 5: Solution Step 2 Graph both radical functions. Step 1 Solve for y. The vertex is (0,0) and the parabola opens right.

Example 6: Solution Step 1 Solve for y Step 2 Graph both radical functions.