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

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.

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.

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

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  …………….

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  ………∞…….

Explore 2

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.

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

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

Assignment 9 P 505 # 1 - 5