4 minutes Warm-Up Identify each transformation of the parent function f(x) = x2. 1) f(x) = x2 + 5 2) f(x) = (x + 5)2 3) f(x) = 5x2 4) f(x) = -5x2 5)

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Presentation transcript:

4 minutes Warm-Up Identify each transformation of the parent function f(x) = x2. 1) f(x) = x2 + 5 2) f(x) = (x + 5)2 3) f(x) = 5x2 4) f(x) = -5x2 5) f(x) = (5x)2 6)

8.6 Radical Expressions and Radical Functions Objectives: -Analyze the graphs of radical functions, and evaluate radical expressions -Find the inverse of a quadratic function

Square-Root Functions Can x be negative? domain: Can f(x) be negative? range:

Example 1 Find the domain of . The domain of is .

Transformations, Vertical stretch or compression by a factor of ; for a < 0, the graph is a reflection across the x-axis. Vertical translation k units up for k > 0 and units down for k < 0. Horizontal stretch or compression by a factor of ; for b < 0, the graph is a reflection across the y-axis. Horizontal translation h units to the right for h > 0 and units to the left for h < 0.

 Example 2 Describe the transformations applied to . y = –2 1 2  Reflect across the x-axis. Stretch vertically by factor of 2. Stretch horizontally by factor of 2. Translate horizontally 1 unit right. Translate vertically 1 unit down.

Example 3 Find the inverse of y = 2x2 – 6. Then graph the function and its inverse together. y = 2x2 – 6 Exchange x and y: x = 2y2 – 6 Write as a quadratic equation in terms of y 2y2 – 6 – x = 0 Solve for y:

Example 3 Find the inverse of y = 2x2 – 6. Then graph the function and its inverse together.

Example 4 You can use the formula to approximate the maximum distance, D, in miles that you can see from a height, x, in feet. Find the maximum distance you can see from heights of 10 feet, 20 feet, and 30 feet.

Cube-Root Functions Can x be negative? domain: Can f(x) be negative? range:

Example 5 Evaluate each expression. a) b)

Practice Evaluate the expression .

Practice Find the domain of the function .

Homework p.525 #11,15,17,23,25,29,33,37,41,45,57,61