What is a reflection in function transformations?

A reflection flips the graph of a function over a specific axis. For example, $$f(x) = -x^2$$ reflects the graph of $$f(x) = x^2$$ over the x-axis.

What is a vertical stretch?

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1. For example, $$f(x) = 2x^2$$ stretches the graph of $$f(x) = x^2$$ vertically by a factor of 2.

What is a vertical compression?

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1. For example, $$f(x) = 0.5x^2$$ compresses the graph of $$f(x) = x^2$$ vertically by a factor of 0.5.

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, $$f(x) = -|x|$$ reflects the graph of $$f(x) = |x|$$ over the x-axis.

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

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

What is the transformation of the function $$f(x) = (x - 3)^2 + 2$$ ?

The function $$f(x) = (x - 3)^2 + 2$$ is shifted right by 3 units and up by 2 units from the parent function $$f(x) = x^2$$ .

What is the transformation of the function $$f(x) = -2(x + 1)^2 - 3$$ ?

The function $$f(x) = -2(x + 1)^2 - 3$$ is reflected over the x-axis, vertically stretched by a factor of 2, shifted left by 1 unit, and down by 3 units.

How do you determine the transformations from the equation $$f(x) = (x - 2)^2 + 4$$ ?

The equation $$f(x) = (x - 2)^2 + 4$$ indicates a right shift of 2 units and an upward shift of 4 units from the parent function $$f(x) = x^2$$ .

Parent Functions & Transformations Flashcard

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear functions (f(x) = x), quadratic functions (f(x) = x^2), and cubic functions (f(x) = x^3).

2.

FLASHCARD QUESTION

Front

What is the equation of the parent quadratic function?

Back

3.

FLASHCARD QUESTION

Front

What is the equation of the parent cubic function?

Back

4.

FLASHCARD QUESTION

Front

What is the equation of the parent absolute value function?

Back

5.

FLASHCARD QUESTION

Front

What does it mean to transform a function?

Back

Transforming a function involves changing its position, shape, or size on a graph through operations such as shifting, reflecting, stretching, or compressing.

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