How would you find the domain and range of x=2^y?
When y = 0 then x = 1.
As y rises towards positive infinity, x rises towards positive infinity.
As y falls towards negative infinity, x falls towards 0.
There is no real value of y corresponding to any negative value of x.
-∞ ≤ y ≤ +∞
0 ≤ x ≤ +∞
your domain should have been
0 < x ≤ ∞
x can never become zero
To find the domain and range of the equation x = 2^y, we need to understand what the equation represents.
Equation x = 2^y is an exponential equation where y is the exponent and 2 is the base. This equation represents the relationship between x and y in an exponential function.
Domain refers to all the possible values that y can take, while range refers to all the possible values that x can take.
In this case, since 2 is a positive number and any positive number raised to any power is always positive, we can conclude that the range of this equation is all positive real numbers (x > 0).
To determine the domain, we need to consider the restrictions on the values of y. In this case, there are generally no restrictions on the values that y can take. Therefore, the domain is all real numbers.
Therefore, the domain of x = 2^y is (-∞, ∞) and the range is (0, ∞).