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Square Root Functions Square Root Functions 0011 0010 1010 1101 0001 0100 1011 Friday – 2/25/11 Section 7-3, Page 424 1 2 45 1 2 45 Graphing Square Root Functions Finding Domains and Ranges The domain of a square root function is limited to the values of x that will keep the radicand (under the square root) nonnegative. 00 11 0 010 1 01 0 110 1 00 01 0 10 0 10 11 The domain and range of a square root function: f ( x) = 2 x + 6 + 2 1. To find the domain write an inequality 2x + 6 ≥ 0 setting the expression under the radical x ≥ −3 greater than or equal to 0, then solve it. 2. To find the range evaluate the value found f (−3) = 2(−3) + 6 + 2 in the domain (-3) in the function. This f (−3) = 2 value is the lower limit of the range. 3. Write the domain and range: Domain: x ≥ 0 Range: f(x) ≥ 2 Find the domain and range of the function f ( x) = 2 x − 5 − 1 1 If a function contains the square root of a variable, it is called a a square root function. Square root functions 00 11 0 010 1 01 0 110 1 00 01 0 10 0 10 11 are a special type of radical function. The function f(x) = x is a curve that starts at (0, 0) and continues towards +∞ as x gets larger. The domain is: x ≥ 0 The range is: f(x) ≥ 0 f ( x) = x The x-int is: x = 0 The y-int is: y = 0 End behavior: As x → 0, f(x) → 0 and As x → +∞, f(x) → +∞ 2 45 The general form of a square root functions is f ( x) = a x − h + k The values h and k determine how the graph shifts and the domain 00 11 0 010 1 01 0 110 1 00 01 0 10 0 10 11 and range of the function: h is the opposite of the value under the radical and will shift the graph right if h is positive and left if h is negative. The domain is x ≥ h. k is the value outside the radical and will shift the graph up if k is positive and down if k is negative. The range is f(x) ≥ k. The value a changes the size and direction of the graph, and if a is negative the graph is reflected over the x-axis. The graph will begin at the point (h, k) and you will need to create a table of values to create a graph. 1 2 45 Examples Graph each square root function, then state the domain and range. f ( x) = −2 x − 2 + 1 x) =1 01x0 +110 3 −1 00 2 01 0 10 0 10 11 00 11f 0(010 x x f(x) f(x) 1 Assignment #3 00 11 0 010 1 01 0 110 1 00 01 0 10 0 10 11 Pg. 427: 4 – 6, 13 – 25, 40, 49 skip 19, 20 Due Tuesday, 3/1/11 2 45 1 2 45 1