Domain and Range

Domain is the interval of x values where the graph exists. Range is the interval of y values where the graph exists. In order to be a function the graph must pass the vertical line test. You use () by ∞ or an open circle. You use [] by the real numbers. #1 polynomials X- Domain: (-∞,∞)-> always! Range: (-∞,∞)-> always! X²- Domain: (-b/2a,∞)-> if it opens upwards Domain: (∞,-b,2a)-> if it opens downwards #2 square roots Domain: 1 set inside the root equal to zero 2 solve 3 plugin (if you get a negative, the interval will not work) 4 write in interval notation Range: [a,∞) #3 square roots Domain: 1 set aside equal to zero 2 solve 3 put the answer in [#,#] Range: If a=0, [0,#²] If a is positive, [0+a,#²+a] If a is negative, [0-a,#²-a] #4 fractions Domain: 1 factor the top and bottom 2 cancel of possible 3 set bottom equal to zero 4 solve x value from step 3 5 write in interval notation, stopping at numbers found in 2 and 3 #5 absolute value Domain: (-∞,∞) Range: If positive or goes upwards, [0+a,∞) If negative or goes downwards, [0-a,∞) Example 1 y = √(x + 4) Domain: [-4,∞) Range: [0,∞) Example 2