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 the direction of the parabola. It represents the maximum or minimum value of the function.

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 and a ≠ 0.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant, given by D = b^2 - 4ac, indicates the nature of the roots of the quadratic equation. 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.

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). This line divides the parabola into two mirror-image halves.

Front

What is the effect of changing the value of 'a' in the quadratic function f(x) = ax^2?

Back

Changing the value of 'a' affects the width and direction of the parabola. If |a| > 1, the parabola is narrower; if 0 < |a| < 1, it is wider. If a < 0, the parabola opens downward.

Front

What is a transformation in the context of functions?

Back

A transformation is an operation that alters the position, size, or shape of a graph. Common transformations include translations, reflections, stretches, and compressions.