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Graphing Square Root Functions
IF. 7 b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
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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.
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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.
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Plot the points on the graph, and connect them with a smooth curve.
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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 …………….
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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 ………∞…….
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Explore 2
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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.
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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
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D. a. horizontal 2 b. horizontal ½ c. horizontal 2 reflection y axis d. horizontal ½ reflection y axis
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Assignment 9 P 505 # 1 - 5
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