Flashcard 5.1

Front

What is the definition of an even function?

Back

A function f(x) is called an even function if for every x in the domain, f(-x) = f(x). This means the graph of the function is symmetric with respect to the y-axis.

Front

What is the definition of an odd function?

Back

A function f(x) is called an odd function if for every x in the domain, f(-x) = -f(x). This means the graph of the function is symmetric with respect to the origin.

Front

How do you find the graph of g(x) = f(-x) from the graph of f(x)?

Back

To find the graph of g(x) = f(-x), reflect the graph of f(x) across the y-axis.

Front

What is the transformation of the graph when a function is reflected across the y-axis?

Back

Reflecting a function across the y-axis changes the sign of the x-coordinates of all points on the graph.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

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 'a' value in a quadratic function determine?

Back

The 'a' value in a quadratic function determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function in standard form f(x) = ax^2 + bx + c is given by the line x = -b/(2a).

Front

What is the formula for the roots of a quadratic equation?

Back

The roots of a quadratic equation ax^2 + bx + c = 0 can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: D = b² - 4ac. It determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.