Question

state the domain and range of the function represented by the graph below. determine if the function is invertible then fill in the sentence for the best possible justification. if the function is invertible, state the domain and range of its inverse. note: the dotted line represents an asymptote, an imaginary line the function gets infinitely close to but never touches. answer attempt 1 out of 2 domain of function: range of function: the function because it in other words, inputs are mapped to output.

Explanation:

Step1: Identify domain from graph

The graph extends horizontally from negative infinity to positive infinity. So the domain is all real numbers.
Domain = $(-\infty,\infty)$

Step2: Identify range from graph

The graph has a horizontal asymptote. It extends vertically from the value of the asymptote (let's assume it's at $y = - 2$) to positive infinity. So the range is $y>-2$, or in interval - notation $(-2,\infty)$.

Step3: Check invertibility

A function is invertible if it is one - to - one. Using the horizontal line test, any horizontal line will intersect the graph at most once. So the function is invertible.

Step4: Find domain and range of inverse

The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.
Domain of inverse = $(-2,\infty)$
Range of inverse = $(-\infty,\infty)$

Answer:

Domain of function: $(-\infty,\infty)$
Range of function: $(-2,\infty)$
The function is invertible because it passes the horizontal line test. In other words, distinct inputs are mapped to distinct outputs.
Domain of inverse: $(-2,\infty)$
Range of inverse: $(-\infty,\infty)$