OpenStudy (anonymous):

What is the domain and range for y=sqrt(x-4)

6 years ago
myininaya (myininaya):

domain is found by solving x-4>=0 the range is found by thinking of the outputs the outputs can range from 0 to infinity

6 years ago
OpenStudy (jim_thompson5910):

Domain: set of all numbers that can be inputted into a function Since you cannot take the square root of a negative number, this means that x-4 CANNOT be negative. So it's either 0 or it's positive. So.. \[x-4\ge0\] \[x-4+4\ge0+4\] \[x\ge4\] So this says: "Any number greater than or equal to 4 will result in x-4 being either 0 or some positive number" So this means that the domain is \[\large \left\{x|x\ge4\right\}\] This basically says: "the domain is the set of all numbers x such that x is greater than or equal to 4" In interval notation, the domain is \[ [4,\infty)\] -------------------------------------------------------- The range is the set of all possible outputs. We can find the most extreme point of the range by plugging in the most extreme value for the domain \[\sqrt{x-4}=\sqrt{4-4}=\sqrt{0}=0\] So the smallest possible output is y=0, which means that the range is \[\large \left\{y|y\ge0\right\}\] This basically says: "the range is the set of all numbers y such that y is greater than or equal to 0" In interval notation, the range is \[ [0,\infty)\]

6 years ago
myininaya (myininaya):

lol wow jim

6 years ago
OpenStudy (jim_thompson5910):

lol yes there's a lot to domain and range

6 years ago