Day 1 examples
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Radical functions have a base graph of y = √x. The domain is all real numbers greater than or equal to 0, and the range is all real numbers greater than or equal to 0. Transformations to the base graph include vertical and horizontal shifts, stretches, and reflections. Standard form for a radical function is y = a√b(x - p) + q, where a stretches vertically, b stretches horizontally, p shifts horizontally, and q shifts vertically.
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Day 1 examples
- 1. Radical Functions Base graph y = √x Domain: Range: applying transformations Ex. y = √x - 2 y = √x - 3 p
- 3. Standard form y = a√b(x - p) + q vertical shift vertical stretch horizontal horizontal if a<0 stretch shift reflects if b<0 in x-axis reflects in y-axis Ex. Graph y = 3√-(x - 1) Step 1: Multiply x-values by 3 Step 2: reflect over y-axis Step 3: horizontal shift 1 unit to right Domain: Range:
- 4. Ex. Graph y - 3 = -√2x Domain: Range: