Need assistance with understanding the rational behind finding domain and range of functions such as 4x^2 and 3/x
Stacey Warren - Expert brainly.com
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domain is the set of x values for which the function exists
range is the set of y values for which the function exists
y=x^2 looks like:
notice here the domain is all real numbers because the curve there exists for all real values on the x-axis
notice the range there is [0,infty) because the curve just isn't there for negative y values
y=-x^2 looks like:
notice the domain is still all real numbers
but the range is (-inf,0] since the graph just does not exist for positive y values
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notice without graphing we can find the domain to be all real numbers but x=1
because we know we cannot divide by 0
and x-1=0 when x=1
...f(1)=1/(1-1)=1/0 <--we have 0 on bottom
you cannot divide by 0
the domain you find visually and algebraically is (-inf,1) union (1,inf)
and notice y=1/(x-1) this will never be 0
so the range is everything by y=0 so you can say that by saying (-inf,0) union (0,inf)
You can see this visually as well: