Question

given the graphed rational function, determine the x - intercept.
\\(0,\frac{3}{2})\\
\\(0, - 4)\\
\\(-4,0)\\
\\(\frac{3}{2},0)\\

Explanation:

Step1: Recall x - intercept definition

The x - intercept of a function is the point where the graph of the function crosses the x - axis. At the x - intercept, the y - coordinate is 0.

Step2: Analyze given points

We are given points \((0,\frac{3}{2})\), \((0, - 4)\), \((-4,0)\), \((\frac{3}{2},0)\). Since the y - coordinate must be 0 for an x - intercept, we can eliminate \((0,\frac{3}{2})\) and \((0, - 4)\) as they have non - zero x - coordinates.

Step3: Check graph

Looking at the graph, we find the point where the function crosses the x - axis. The graph crosses the x - axis at the point where \(x=-4\) and \(y = 0\), which is the point \((-4,0)\).

Answer:

C. \((-4,0)\)