state the domain and range of the function represented by the graph below. determine if the function is…
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.
Answer
Explanation:
Step1: Determine the domain
The graph extends infinitely to the left and right along the x - axis. So the domain is all real numbers, which can be written as $(-\infty,\infty)$.
Step2: Determine the range
The lowest point of the graph is at $y = 1$ and it extends upwards infinitely. So the range is $[1,\infty)$.
Step3: Check invertibility
A function is invertible if it passes the horizontal - line test. A horizontal line can intersect this graph at more than one point. So the function is not invertible.
Answer:
Domain: $(-\infty,\infty)$ Range: $[1,\infty)$ Invertible: No Justification: Fails the horizontal - line test.