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, ∞).