Note: As you missed to mention the graph for f(x) = x + 1 from where we had to check which option defines the accurate graph. But, after a little research, I was able to get the graph of this question, and hence attaching the graph. So, I am answering based on that graph which, anyways, would clear your concept about determining the domain of the function that shows in a graph.
Answer:
x > 1 is the domain of the f(x) = x + 1.
Step-by-step explanation:
A domain is the set of all x values that a function passes through. It means a domain is set of all input values where the function is defined, meaning whatever you input the x value, for every x-value there is only one y-value that corresponds to it.
So, now lets talk about the given function f(x) = x + 1 and its graph as shown in attached figure. Carefully observe the top right part of the graph of f(x) = x + 1. It is validating the condition of x > 1.
For example,
Just input some x values, greater than 1 i.e. x > 1, in f(x) = x + 1 to determine the output values.
For example, for x > 1
- For x = 2, f(x) = 3. So, the graph must pass through of P(2, 3)
- For x = 3, f(x) = 4. So, the graph must pass through of P(3, 4)
- For x = 4, f(x) = 5. So, the graph must pass through of P(4, 5)
and so on.
So, the top right part of the graph of f(x) = x + 1 is validating the condition of x > 1 as it is passing through P(2, 3), P(3, 4) and P(4, 5) etc. and so on.
So, x > 1 is the domain of the f(x) = x + 1.
Keywords: domain, function
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