How do you find the domain and range for #y=2x-10#?

1 Answer
May 5, 2016

Answer:

The domain and range are both #RR# (all real numbers).

Explanation:

The domain consists of all possible valid #x#-values, while the range consists of all possible #y#-values.

As #2x-10# is defined for all real numbers, the domain of #2x-10# is #RR#.

We would have to limit our domain if there was the possibility of dividing by #0# such as in #1/x# for #x=0#, taking an even root of a negative number, such as #sqrt(x)# for #x<0#, or taking the logarithm of a non-positive number, such as #ln(x)# for #x <= 0#. As none of these apply, we do not have any restrictions on our choice of #x#.

Note that #2((y+10)/2)-10 = y#, and thus for any real #y#, we may choose #x = (y+10)/2# to get #y = 2x-10#. As such, every real number #y# is in the range of the function.