Step-by-step explanation:
remember, the domain is the interval or set of all valid x values, the range is the interval or set of all valid y values (functional result values).
1.
domain : -infinity < x < +infinity
range : -1 <= y < +infinity
due to the x² term that part can never be negative. the minimum is 0, and then -1 gives us a overall minimum -1. and then up ... the sky is the limit ...
2.
domain : every value of x that does not turn (3x + 5) to 0 and therefore does not cause a 1/0 situation.
the only forbidden value of x is therefore
3x + 5 = 0
3x = -5
x = -5/3
so, (-infinity < x < -5/3) OR (-5/3 < x < +infinity)
range : -infinity < y < +infinity
3.
domain : -infinity < x < +infinity
range : 0 <= y < +infinity
due to the x⁴ term (even exponent) all results will be positive starting with 0. similar to 1.
4.
this is 1/(2x) as I understand it.
similar to 2. we must avoid at 1/0 situation.
so, x must not be 0. everything else is possible
domain : (-infinity < x < 0) OR (0 < x < +infinity)
range : -infinity < y < +infinity
5.
everything is allowed and possible.
domain : -infinity < x < +infinity
range : -infinity < y < +infinity
