In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

Key Concepts

X-Intercepts

X-intercepts are the points where a graph crosses the x-axis. At these points, the value of y is zero. To find the x-intercepts, one can set the function equal to zero and solve for x. In graphical terms, these are the horizontal intersections of the curve with the x-axis.

Y-Intercepts

Y-intercepts are the points where a graph crosses the y-axis, where the value of x is zero. To determine the y-intercept, substitute x = 0 into the function and solve for y. Graphically, these points represent the vertical intersections of the curve with the y-axis.

Graph Interpretation

Graph interpretation involves analyzing the visual representation of a function to extract meaningful information, such as intercepts, trends, and behavior at extremes. Understanding how to read the axes, tick marks, and the shape of the graph is crucial for accurately identifying key features like intercepts and overall function behavior.