Final answer:
Since both functions, f(x) = 2x - 4 and 4x² - 16, are continuous, there are no breaks or points of discontinuity in their graphs. The graphs will be smooth and without any abrupt changes in direction.
Step-by-step explanation:
To examine the continuity of the function f(x) = 2x - 4 in relation to the function 4x² - 16, we need to check if there are any points of discontinuity or breaks in the graph.
1. Continuity of f(x): The function f(x) = 2x - 4 is a linear function, which means it is continuous everywhere. Linear functions have a constant rate of change and a straight line graph without any jumps or holes. Therefore, f(x) = 2x - 4 is continuous for all real values of x.
2. Continuity of 4x² - 16: The function 4x² - 16 is a quadratic function, which is also continuous everywhere. Quadratic functions have a smooth, curved graph without any sudden changes or discontinuities.