Click the Secant Line, Slope of Secant, and Values boxes. Set the \( x \)-slider to the point \( x=4.5 \) and the \( x+h \)-slider to 6.5. Complete parts 1 through 3 below. Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure. Part 1: What is the value of \( f(x+h)-f(x) \) ? \( f(x+h)-f(x)= \)

To find \( f(x+h) - f(x) \), first, determine the values of \( f(4.5) \) and \( f(6.5) \) using the interactive figure. Calculate the difference: \( f(6.5) - f(4.5) \). This will give you the value of \( f(x+h) - f(x) \). For example, if \( f(4.5) = 10 \) and \( f(6.5) = 15 \), then \( f(6.5) - f(4.5) = 15 - 10 = 5 \). The slope of the secant line can be determined by taking this difference and dividing it by \( h \), where \( h \) is the difference between your \( x \)-slider and your \( x+h \)-slider. Enjoy exploring the interactive features to unveil the answers! By understanding secant lines, you're diving into foundational concepts in calculus that have vast applications. From physics to economics, approximating changes using secant lines helps in analyzing trends without needing to solve complex equations! Mathematically, secant lines represent the average rate of change between two points on a function, making them essential in understanding motion, growth, and decay. This concept sets the stage for the amazing world of derivatives, which detail instantaneous change—think of it as the thrilling next step in your mathematical adventure!