What is a horizontal stretch?

A horizontal stretch increases the distance of points from the y-axis. For example, if $$f(x)$$ is stretched by a factor of 2, the new function is $$f(\frac{x}{2})$$ .

What is a horizontal compression?

A horizontal compression decreases the distance of points from the y-axis. For example, if $$f(x)$$ is compressed by a factor of 1/2, the new function is $$f(2x)$$ .

How do you identify the vertex of a quadratic function in vertex form?

The vertex of a quadratic function in the form $$y = a(x - h)^2 + k$$ is the point (h, k).

What is the general form of a quadratic function?

The general form of a quadratic function is $$y = ax^2 + bx + c$$ , where a, b, and c are constants.

What is the significance of the 'a' value in a quadratic function?

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a

What is the axis of symmetry in a quadratic function?

The axis of symmetry of a quadratic function in the form $$y = ax^2 + bx + c$$ is given by the line $$x = -\frac{b}{2a}$$ .

How do you find the x-intercepts of a quadratic function?

To find the x-intercepts of a quadratic function, set $$y = 0$$ and solve the equation $$ax^2 + bx + c = 0$$ using factoring, completing the square, or the quadratic formula.

What is the difference between a function and its inverse?

A function maps inputs to outputs, while its inverse reverses this mapping, meaning if $$f(a) = b$$ , then $$f^{-1}(b) = a$$ .

Precalculus Review - Transformations Flashcards

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FLASHCARD QUESTION

Front

What is a transformation in the context of functions?

Back

A transformation refers to the alteration of a function's graph through operations such as translation, reflection, stretching, or compression.

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