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

If f(x) = x^2 - 5x, what is f(4)?

Back

f(4) = 4^2 - 5(4) = 16 - 20 = -4.

Front

If f(x) = 6x^2 - 4, what is f(-1)?

Back

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

Front

If f(x) = 3x^2 - 11, what is f(-5)?

Back

f(-5) = 3(-5)^2 - 11 = 3(25) - 11 = 75 - 11 = 64.

Front

If g(x) = 5 - 6x, what is g(-5)?

Back

g(-5) = 5 - 6(-5) = 5 + 30 = 35.

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 is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a quadratic function has a variable rate of change and graphs as a parabola.