Question

"Suppose a plant grows one inch every year. If x is how old the plant is (in years), and f (x) is how tall the plant is (in inches), what type of function is f (x)?

a. Absolute Value Function
b. Identity Function
c. Quadratic Function
d. Constant Function
e. Square Root Function"

Answer 1

The function representing a plant that grows one inch every year where 'x' is the age and 'f(x)' is the height, would be an identity function since the height directly corresponds to the age.

Step-by-step explanation:

If we consider that a plant grows one inch every year, where x is the age of the plant in years, and f(x) is the height of the plant in inches, then we can describe f(x) as a function of x. Since the plant grows at a constant rate, for each year that passes, the plant height increases by one inch, which is a linear relationship. Therefore, the function that describes the height of the plant as it grows over time would be an identity function, because the height of the plant is directly equivalent to its age (in inches).

The function f(x) = x is a linear function with a slope of 1 and a y-intercept of 0. This means for every increase of 1 in x, f(x) also increases by 1. This denotes a linear growth rate, one that is consistent and straight, which is depicted as a straight line when graphed. Hence, the correct answer is (b) Identity Function.