Question

unit: functions progress: the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. which of the following is a graph of $f(x) = -4 + \sqrt{x}$? images of four graphs are shown here unit test: functions functions

Explanation:

Step1: Analyze the domain of the function

The function is \( f(x)= - 4+\sqrt{x}\). The square root function \(\sqrt{x}\) is defined for \(x\geq0\), so the domain of \(f(x)\) is \(x\geq0\). This means the graph should only exist for non - negative \(x\) - values. So we can eliminate the graphs where \(x < 0\) has a part of the curve (the third and fourth graphs as they have parts for \(x<0\)).

Step2: Find the y - intercept

To find the y - intercept, we set \(x = 0\) in the function \(f(x)=-4+\sqrt{x}\). Then \(f(0)=-4+\sqrt{0}=-4\). So when \(x = 0\), \(y=-4\).

Now let's check the first two graphs:

• For the first graph, when \(x = 0\), the \(y\) - value is \(4\) (not \(-4\)), so it is not the graph of our function.
• For the second graph, when \(x = 0\), the \(y\) - value is \(- 4\) (matches \(f(0)=-4\)) and the domain is \(x\geq0\) (since the graph starts at \(x = 0\) and goes for \(x>0\)). Also, as \(x\) increases, \(\sqrt{x}\) increases, so \(f(x)=-4 + \sqrt{x}\) increases as \(x\) increases, which is consistent with the shape of the second graph.

Answer:

The second graph (the middle - most of the four graphs)