In Exercises 85–90, find the x-intercepts of the graph of each equation. Then use the x-intercepts to match the equation with its graph. [The graphs are labeled (a) through (f).] y = √(x - 4) + √(x + 4) - 4

Key Concepts

X-Intercepts

X-intercepts are the points where a graph intersects the x-axis, which occurs when the value of y is zero. To find the x-intercepts of an equation, you set y equal to zero and solve for x. This is crucial for understanding the behavior of the graph and identifying key points that help in graphing the function.

Square Root Functions

Square root functions, such as y = √(x - a), are defined for values of x that make the expression under the square root non-negative. This means that the domain of the function is limited to x values greater than or equal to a. Understanding the domain is essential for determining where the function is valid and for finding x-intercepts.

Graph Matching

Graph matching involves comparing the characteristics of a function's graph with given options to identify the correct representation. This requires understanding the shape and key features of the graph, such as intercepts, asymptotes, and overall behavior. By analyzing the x-intercepts and other properties, one can effectively match the equation to its corresponding graph.