Evaluating Functions

Front

What is the definition of a function in mathematics?

Back

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

Front

What does it mean to evaluate a function at a specific point?

Back

Evaluating a function at a specific point means substituting the input value into the function's formula to find the corresponding output value.

Front

How do you evaluate f(x) = x^2 for f(-8)?

Back

Substitute -8 into the function: f(-8) = (-8)^2 = 64.

Front

What is the formula for a quadratic function?

Back

A quadratic function is generally expressed as f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you evaluate f(x) = 6x^2 - 4 for f(-1)?

Back

Substitute -1 into the function: f(-1) = 6(-1)^2 - 4 = 6(1) - 4 = 2.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How do you find f(-5) for the function f(x) = 3x^2 - 11?

Back

Substitute -5 into the function: f(-5) = 3(-5)^2 - 11 = 3(25) - 11 = 75 - 11 = 64.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How do you evaluate f(t) = -2t^2 + 1 for f(2)?

Back

Substitute 2 into the function: f(2) = -2(2)^2 + 1 = -2(4) + 1 = -8 + 1 = -7.

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.