f(x) is an exponential growth function. It can be modeled as [tex]f(x) = a(1 + r)^{t} [/tex], where a is the initial amount, r is the interest rate in decimal form, and t is the time period. When the values from the scenario are plugged in, it looks like [tex]f(x) = 6(1.05)^{t}[/tex]. On a graph, a will be the y-intercept, so the y-intercept of f(x) is 6.
g(x) has a y-intercept that must be less than 6. The function reaches a y-value of 6 when x = 1, not 0 (when x = 0, we are given the y-intercept). We see that as y decreases x decreases, so it is confirmed that g(x) has a y-intercept that is < 6. Already we know that its y-intercept is less than that of f(x).
h(x) visibly intercepts the y-axis at y = 4. Its y-intercept is 4.
j(x) is written in exponential growth format (like f(x)), where the initial amount, a, would be the y-intercept. 10 is its y-intercept.
After evaluating the y-intercepts of each of these functions, it is determined that j(x) has the highest y-intercept.
