Evaluating Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean to evaluate a function?

Back

To evaluate a function means to calculate the output of the function for a specific input value.

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 evaluate f(x) = 2x + 3 for x = 4?

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

Front

What is the value of f(2) if f(x) = x^2 + 1?

Back

f(2) = 2^2 + 1 = 4 + 1 = 5.

Front

What is the quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.

Front

Evaluate f(x) = -2x^2 + 1 for f(2).

Back

f(2) = -2(2)^2 + 1 = -8 + 1 = -7.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function.

Front

Evaluate f(x) = 2x^2 + 5x - 17 for f(-1).

Back

f(-1) = 2(-1)^2 + 5(-1) - 17 = 2 - 5 - 17 = -20.

Front

What is the standard form of a quadratic function?

Back

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