Exam 5 Review- Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs, known as the domain.

Front

What is the notation for a function?

Back

Functions are typically denoted by letters such as f, g, or h, followed by the input in parentheses, e.g., f(x).

Front

How do you find the composition of two functions, f and g?

Back

The composition of two functions f and g, denoted as f(g(x)), is found by substituting g(x) into f.

Front

What is the maximum height of a projectile?

Back

The maximum height of a projectile can be found using the vertex formula for a quadratic function, h = -16t^2 + vt + h0, where v is the initial velocity and h0 is the initial height.

Front

What is the inverse of a function?

Back

The inverse of a function f, denoted as f^-1, is a function that reverses the effect of f, meaning if f(a) = b, then f^-1(b) = a.

Front

How do you find the inverse of a function given points?

Back

To find the inverse of a function given points (a, b), swap the coordinates to get (b, a).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function.

Front

How do you determine the time it takes for an object to reach maximum height?

Back

For a quadratic function in the form h = -16t^2 + vt + h0, the time to reach maximum height is given by t = -b/(2a), where a and b are coefficients from the equation.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation: if positive, two real roots; if zero, one real root; if negative, no real roots.