Question

What is the domain and range of `y=-5^x` ?

What is the domain and range of `y=-5^x` ?

Answer 1

Domain: `(-oo,oo)` Range: `(-oo,0)`

Explanation:

By default, the domain of the exponential function, or the `x` values for which it exists, is `(-oo, oo)`

The range of the parent exponential function, `y=b^x,` where `b` is the base, is `(0,oo)` because by default, the exponential function can never be negative or zero, but it keeps increasing forever.

Here, `b=-5`. The negative implies that we've flipped the graph of our function about the `x`-axis; therefore, our range will be `(-oo,0)`, because our function will never be positive (the negative sign ensures that) or zero and keeps decreasing forever due to the negative.