Answer:
Step-by-step example explanation:
DOMAIN:
{
x
∣
x
≠
3
2
}
RANGE:
{
y
∣
y
≠
3
2
}
Explanation:
The domain consists of all numbers you can legally plug into the original. The excluded "illegal" values would be dividing by zero or negatives under square roots.
This expression has a denominator, so there is a risk of illegally dividing by zero. This would happen only if
2
x
−
3
=
0
2
x
=
3
x
=
3
2
This means that
x
=
3
/
2
is excluded from the domain. Therefore,
Domain: All real numbers except
x
=
3
/
2
. More formally, you could state the domain as
{
x
∣
x
≠
3
2
}
.
For rational functions, you find the range by evaluating the degree of the numerator compared to the degree of the denominator. If the degree of the top > degree of bottoms, then you have a horizontal asymptote at
y
=
0
. If they are equal, you have a horizontal asymptote. The coefficient of highest degree in the numerator is divided by the coefficient of the highest degree on the bottom. The result is
y
=
that fraction. So in our case, you have a horizontal asymptote at
y
=
3
2
