Square Root Functions and Log Functions SQUARE ROOT FUNCTIONS AND LOG FUNCTIONS
Algebra 2 Learning Targets
1. Graph the parent function f  x   x
2. Identify the anchor points on the parent square root function.
3. Apply transformations to f  x   x to draw the graph of the transformed function.
4. Describe the transformations when given the transformed equation of a square root function.
5. Write the equation when given a description of the transformation to the parent square root function
6. Understand where the graph of a log function came from.
Example 1: Find the inverse of the parent function of a quadratic. f  x   x 2
Find the inverse of the graph and the inverse equation. What do you notice?
Example 2: Graph the parent function f  x  
values.
a) What is the domain?
x by completing the table of
x
0
1
4
y
b) What is the range?
The transformation rules we have used in the past continue to work the same way.
Example 3: For each function below, describe the transformation of the square root function and then graph it.
a) g ( x ) = x - 2 + 3
x
y
0
1
4
9
0
1
2
3
New New
x
y
b) h ( x ) = -3 x
x
y
New New
x
y
Square Root Functions and Log Functions Algebra 2 Example 4: Use the following description to write the new function: “The parent function f  x  
the x-axis and translated right 8 units.”
x is reflected across
Example 5: Use the following description to write the new function: “The parent function f  x  
stretched by a factor of 7 and translated up 12 units.”
x is vertically
Example 6: Find the inverse of the parent function of a exponential. f  x   2 x
Find the inverse of the function graphically.
State the domain and range of the function.
What else changed?