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Graph the function .
Identify and analyze attributes of square root functions, including
Domain and range
Maximum and minimum (endpoint/starting point)
Direction (right or left)
Describe attributes as seen in various representations:
Graph a function and its inverse.
By hand using a table or reflection about y = x.
On calculator (using L1 and L2)
Write the inverse function algebraically
Interchange x and y, then solve for y
Use notation such as f-1(x).
Discover the graph of a square root function as the inverse of a quadratic function, with restrictions.
Compare the domain and range of a relation or function and its inverse.
Analyze inverse relations and functions.
From a situation (i.e: the area of an equilateral triangle in terms of its base length) by reversing the independent and dependent variables
Calculator (table and graph)
Patty paper (optional)
Use the vertical line test to determine whether or not the inverse is a function.
Restrict the domain for 1 to 1 correspondence.
Determine the effect on the graph of when f(x) is replaced by:
af(x): vertical compression/expansion and/or reflection over x-axis
f(x) + d: vertical translation
f(bx) : horizontal compression/expansion and/or reflection over y-axis
f(x - c): horizontal translation for specific positive and negative values of a, b, c, and d.
Predict changes to the graph when a, b, c, or d are changed.
Connect the effects of changing a, b, c, or d to a problem situation.
Use transformations to sketch square root functions.
Verify parameter changes on graphing calculator.
Express limitations on the domain and range of square root functions.
Determine the equation of a transformed square root function from a graph.
Describe attributes of a transformed square root functions as seen in various representation.