To find the range of the function f(x) = √x - 7, we need to consider the domain of the function, which is the set of all possible input values that we can use in the function. Since the square root of a number must be non-negative, the domain of this function is x ≥ 49.
Next, we need to evaluate the function for different values of x within the domain to see what values it produces. For example, if we plug in x = 49, we get f(49) = √49 - 7 = 7 - 7 = 0. If we plug in x = 50, we get f(50) = √50 - 7 = 7.236 - 7 = 0.236. As we can see, the function takes on both positive and negative values within its domain, so the range is all real numbers.
To represent this visually, we can plot the function on a graph and see how its values vary as the input x changes. We can use a graphing calculator or other graphing technology to do this. On a graph, the x-axis represents the input values (the domain of the function), and the y-axis represents the output values (the range of the function).
Here is a graph of the function f(x) = √x - 7:
[Insert graph here]
As we can see from the graph, the range of the function is all real numbers, indicated by the fact that the graph extends to both positive and negative infinity on the y-axis. This tells us that the range of the function is y .