Math 3 EOC review 2a

Front

What is a function with an inverse that is also a function?

Back

A function is one-to-one (bijective) if it has an inverse that is also a function. For example, the function f(x) = \frac{x-5}{3} is one-to-one.

Front

What is the first step in finding the inverse of a function?

Back

The first step is to swap x and y in the equation of the function.

Front

How do you determine the year when a population reaches a certain number with a constant growth rate?

Back

Use the formula for exponential growth: P(t) = P_0(1 + r)^t, where P_0 is the initial population, r is the growth rate, and t is the number of years.

Front

What is the quotient of (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

The quotient is 2x^2 - x + 3.

Front

How do you evaluate a function at a specific point?

Back

Substitute the value into the function's equation. For example, for f(x) = 6x^2 - 4, to find f(-1), substitute -1 for x.

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes x to y, then f^(-1)(y) takes y back to x.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

What is the significance of the growth rate in population models?

Back

The growth rate determines how quickly the population increases over time, affecting future population estimates.

Front

What is the process of polynomial long division?

Back

Polynomial long division involves dividing the leading term of the dividend by the leading term of the divisor, then multiplying and subtracting until the remainder is less than the divisor.

Front

What is the formula for exponential growth?

Back

The formula is P(t) = P_0(1 + r)^t, where P_0 is the initial amount, r is the growth rate, and t is time.