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I recommend using a graphing calculator. If you don't have something like a TI83, then you can use a free graphing website like desmos https://www.desmos.com/calculator
i have one, i can graph them, i just really need help with the domain and range.
do you see how the graph extends infinitely in both directions in the horizontal (x axis) direction?
What that tells us is that the domain is the set of all real numbers. You can plug in any number you want for x and it's a valid input.
yes, it suppose to look wavy too right? since i graph it in radian?
yes it goes up and down
okay good. so the domain would just be all real numbers?
how about the range?
you sure? every y value is a possible output?
wait, will it be (0,5) since that the only whole y number i got?
look at the lowest and highest points. What are the y coordinates of those points?
im lost at this point, the X values go on forever, how do i find the highest and lowests?
here is the sine curve |dw:1439769652243:dw|
how about the y coordinate for this point |dw:1439769836217:dw|
so wait, the range is between the 2 most nearest whole numbers?
the range is between -6 and -4 because these are the possible y values that pop out of the function. No other y value is possible. We can't have y = 0 for instance
we write the range as \[\Large -6 \le y \le -4\] which in interval notation is [-6,-4]