Christina has some money at home, and the amount is modeled by the function h (x) = 103. She read about a bank that has savings accounts that accrue interest according to the function s (x) = (1.03) x - 1. Using complete sentences, explain to Christina how she can combine her functions to create a new function, and explain what this new function means.

X usually represents time in months, and when you say h (x) = 103, this is a constant function, flat all throughout as x→∞. For s (x), it represents a line with increasing value of s (x) as x→∞ at a rate of 1.03 and intercept of - 1 at s (x) axis. When you say "combine" to form a new function means the addition of the two given functions, that is, h (x) + s (x), say equal to g (x).

g (x) = h (x) + s (x) = 103+1.03x-1=1.03x+102 g (x) = 1.03x+102

The new function g (x) is the same as s (x) with respect to the rate of increase, equal to 1.03, except this time, the intercept is + 102, g (x) is the shifted version of s (x), from - 1 to + 102 (due to h (x) = 103). Her savings account in a bank will grow at a rate of 3% per unit of time (x), starting at a savings of 102 at x=0.