Quarter Test Review

Front

What is the formula for continuous compound interest?

Back

The formula for continuous compound interest is A = Pe^(rt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and t is the time the money is invested for in years.

Front

How do you solve a quadratic equation using the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the quadratic equation ax² + bx + c = 0.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function f^(-1)(x) that reverses the effect of f. If f(a) = b, then f^(-1)(b) = a.

Front

How do you find the x-intercept of a function?

Back

To find the x-intercept of a function, set y = 0 and solve for x.

Front

What is the inverse of the function R(x) = 2x + 1?

Back

R^(-1)(x) = (x - 1) / 2.

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; in other words, f(a) = f(b) implies a = b.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

What is the formula for the area of a circle?

Back

The area A of a circle is given by A = πr², where r is the radius of the circle.

Front

How do you determine if a function is even or odd?

Back

A function f(x) is even if f(-x) = f(x) for all x in the domain. It is odd if f(-x) = -f(x) for all x in the domain.

Front

What is the relationship between a function and its inverse?

Back

The relationship is that if f(x) is a function and f^(-1)(x) is its inverse, then f(f^(-1)(x)) = x and f^(-1)(f(x)) = x for all x in the domain.