What is a horizontal compression?

A horizontal compression occurs when the input values of a function are multiplied by a factor between 0 and 1. For example, transforming $$f(x)$$ to $$f(k \times x)$$ , where $$0

How do you identify the vertex of a quadratic function?

The vertex of a quadratic function in the form $$f(x) = a(x - h)^2 + k$$ is the point (h, k). It represents the maximum or minimum point of the parabola.

What is the parent function of a cubic function?

The parent function of a cubic function is $$f(x) = x^3$$ . It has a characteristic S-shaped curve.

What is the effect of a negative sign in front of a function?

A negative sign in front of a function reflects the graph over the x-axis. For example, transforming $$f(x)$$ to $$-f(x)$$ flips the graph vertically.

What does the equation $$f(x) = (x - 3)^2 + 2$$ represent?

This equation represents a parabola that has been shifted right by 3 units and up by 2 units from the parent function $$f(x) = x^2$$ .

What is the transformation represented by $$f(x) = -2(x + 1)^3 - 4$$ ?

This transformation reflects the cubic function over the x-axis, stretches it vertically by a factor of 2, shifts it left by 1 unit, and down by 4 units.

How do you determine the transformations of a square root function?

For a square root function in the form $$f(x) = a\text{sqrt}(x - h) + k$$ , the transformations include a vertical stretch/compression by $$a$$ , a horizontal shift by $$h$$ , and a vertical shift by $$k$$ .

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

The value of 'a' determines the vertical stretch or compression of the function. If |a| > 1, the function is stretched; if 0

Function Transformations Review Flashcards

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FLASHCARD QUESTION

Front

What is a function transformation?

Back

A function transformation refers to the changes made to the graph of a function, which can include shifts, stretches, compressions, and reflections.

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