1. Graphing Square Root Functions
IF. 7 b. Graph square root, cube root, and piecewise-defined functions, including step functions and
absolute value functions.

2. Essential Question
How can you use transformation of a parent square root function to graph functions of the form g(x) = a √ (x – h) + k.

3. Explore: Graphing and Analyzing the Parent Square Root Function
The domain of the square root function (limited to real numbers) is given by {x | x ≥ 0}
Fill in the table.

4. Plot the points on the graph, and connect them with a smooth curve.

5. Write the range of this square root function:
{ y | y ≥ …….. }
The graph appears to be getting flatter as x increases, indicating that the rate of change ……… as x increases.
Describe the end behavior of the square root function, f (x) = √x.
f (x) …………. as x  …………….

6. Write the range of this square root function:
{ y | y ≥ …0….. }
The graph appears to be getting flatter as x increases, indicating that the rate of change decreases……… as x increases.
Describe the end behavior of the square root function, f (x) = √x.
f (x) ……∞……. as x  ………∞…….

7. Explore 2

8. B. Predict the effect of the parameter k on the graph of g(x) = √(x) + k for each function.
a. g(x) = √(x) + 2: The graph is a …………………… of the graph of f(x) [right/ left/ up/ down] 2 units.
b. g(x) = √(x) – 2: The graph is a …………………… of the graph of f(x) [right/ left/ up/ down] 2 units.

10. Answers A. a. translation right b. translation left
B. a. translation up
b. translation down
C. a. vertical 2
b. vertical ½
c. vertical ½ reflection x axis
d. vertical 2 reflection x axis

12. D. a. horizontal 2
b. horizontal ½
c. horizontal 2 reflection y axis
d. horizontal ½ reflection y axis

13. Assignment 9
P 505 # 1 - 5