Lesson 3: 5-4 Graphing Square Root Functions

What are the domain and range of the parent square root function?
How do you find the domain of a square root function that has been transformed in the plane?

square root functions
radical function

F.IF.4 For a function that models a relationship between two quantities, interpret dey features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.IF.7b Graph square root, cube root, and piecewise defined functions, including step function and absolute value functions
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx) and f(x+k) for specific values of k; find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

see below

A function that contains a variable inside a square root symbol is called a square root function. The domains and ranges of these functions are limited to values for which the function is defined.

With guitar, pitch is dependent on string length and string tension. The longer the string is, the higher the tension needs to be to produce a desired pitch. Likewise, the heavier the string is, the higher the tension needs to be to reach a desired pitch. This can be modeled by the square root functions f=(1/2L)(T/)^(1/2) where T is the tension, P is the mass of the string, L is the length of the string, and f is the pitch.

for ex 51, remind students to graph y=(5x+10)^(1/2) and then compare graphs

Have students work in pairs of small groups to discuss how to graph square root functions such as those in exercises 19-28. Students should discuss how to determine the domain and range of a functions, and how to find the inverse of square functions.

Use McGraw Hill resources

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