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 parentheses containing the input value, e.g., f(x).

Front

How do you 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 value of f(-1) if f(x) = 6x^2 - 4?

Back

f(-1) = 6(-1)^2 - 4 = 6 - 4 = 2.

Front

Evaluate the function f(x) = 3x + 2 for f(2).

Back

f(2) = 3(2) + 2 = 6 + 2 = 8.

Front

If h(a) = 3 - 2a^2, what is h(-3)?

Back

h(-3) = 3 - 2(-3)^2 = 3 - 2(9) = 3 - 18 = -15.

Front

What is the value of f(4) if f(x) = 4x + 5?

Back

f(4) = 4(4) + 5 = 16 + 5 = 21.

Front

What is the general form of a quadratic function?

Back

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

Front

What does the 'a' in a quadratic function determine?

Back

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