Create a graph with age on the x-axis and money spent on a night out on the y-axis. Plot the ordered pairs as a scatter plot. After placing all points, state the relationship, for example: "the older someone is, the less money they spend on a night out," ensuring the description matches the plotted data. (:
The blue line depicted in the attached image illustrates the reflection of f(x) across the x-axis.
To elucidate, the function f(x) is an exponential function displaying the characteristics: the y-intercept calculates as f(0) = 6(0.5)⁰ = 6; the multiplicative rate of change is 0.5, signifying a decay function (decreasing); and the horizontal asymptote exists at y = 0, defining the limit of f(x) as x approaches positive infinity. The reflection across the x-axis for f(x) results in a function denoted as g(x) = -f(x), leading to g(x) reflecting the features discussed including growth into the third quadrant while never intersecting the x-axis. Therefore, using these insights, it is feasible to sketch the corresponding graph across the x-axis.
