Question

An exponential function has the equation f(x)=−3x−2
. Complete the inequality to show the range of the function.

(1 point)
The range of the function is y

Answer 1

Do you mean an exponential with the exponent (x − 2) or with −2 as a vertical shift? The symbol you wrote is ambiguous. Here are the common interpretations:

- If f(x) = −3^{x−2} (i.e. −(3^{x−2})), then 3^{x−2} > 0 so f(x) < 0. Range: y < 0.

- If f(x) = −3^{x} − 2 (i.e. −(3^{x}) − 2), then −3^{x} < 0 and shifting down 2 gives f(x) < −2. Range: y < −2.

- If you meant the linear function f(x) = −3x − 2, then the range is all real numbers: y ∈ (−∞, ∞).

Tell me which form you intended and I’ll confirm.