Answer :
Answer:
Step-by-step explanation:
Linear, quadratic, and exponential functions are all fundamental types of functions studied in algebra, each with its own distinct characteristics.Linear Functions:Features: Linear functions have a constant rate of change, meaning they increase or decrease at a constant rate. They have a straight-line graph.Uniqueness: Linear functions can be represented by the equation f(x)=mx+bf(x)=mx+b, where mm is the slope of the line and bb is the y-intercept. They describe relationships that are directly proportional and exhibit constant change over equal intervals.Quadratic Functions:Features: Quadratic functions have a squared term (e.g., x2x2) in their equations. They often form a parabolic curve when graphed.Uniqueness: Quadratic functions have a constant second difference (or rate of change of the rate of change). They can model various real-world situations, including projectile motion, certain economic relationships, and the shape of certain physical objects like satellite dishes.Exponential Functions:Features: Exponential functions have a constant base raised to a variable exponent (e.g., bxbx), where the base is a positive real number greater than 1.Uniqueness: Exponential functions exhibit rapid growth or decay. They are characterized by a constant ratio of change, meaning they increase or decrease by the same percentage over equal intervals. Exponential growth occurs when the base is greater than 1, while exponential decay occurs when the base is between 0 and 1.
