Math 3 EOC review 2a

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function. If the function f takes an input x and produces an output y, then the inverse function f^-1 takes y as input and produces x as output.

Front

How do you find the inverse of a function graphically?

Back

To find the inverse of a function graphically, reflect the graph of the function across the line y = x.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is P(t) = P₀e^rt, where P₀ is the initial amount, r is the growth rate, and t is time.

Front

What does the function h(x) = 125x represent in the context of purchasing sneakers?

Back

The function h(x) = 125x represents the total cost of purchasing x sneakers at $125 each before tax.

Front

What is the discount function j(x) = 0.30(125x) used for?

Back

The function j(x) = 0.30(125x) calculates the total discount applied to the cost of x sneakers.

Front

How do you calculate the cost after applying a discount?

Back

To calculate the cost after applying a discount, subtract the discount from the original price: m(x) = h(x) - j(x).

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Front

What is the value of 2^x if x = 2 log₂(3/4)?

Back

2^x = 2^{2 log₂(3/4)} = (3/4)² = 9/16.

Front

What is the formula for population growth?

Back

The formula for population growth is P(t) = P₀(1 + r)^t, where P₀ is the initial population, r is the growth rate, and t is time.

Front

How do you determine the year when a population will reach a certain number?

Back

To determine the year when a population will reach a certain number, use the population growth formula and solve for t, then add t to the initial year.