What does the transformation $$g(x) = x^2 - 5$$ indicate about the graph of $$f(x) = x^2$$ ?

The graph of $$f(x)$$ is shifted down 5 units.

What is the result of the transformation $$f(x) - 3$$ ?

The graph of $$f(x)$$ shifts down 3 units.

What does the transformation $$f(x) = x^2$$ to $$g(x) = (x - 5)^2$$ indicate?

The graph of $$f(x)$$ shifts right 5 units.

What is the effect of the transformation $$f(x) = x^2$$ to $$g(x) = (x + 5)^2$$ ?

The graph of $$f(x)$$ shifts left 5 units.

What does the transformation $$f(x) = x^2$$ to $$g(x) = -x^2$$ indicate?

The graph of $$f(x)$$ is reflected over the x-axis.

What is the effect of a vertical stretch on a function?

A vertical stretch increases the distance of points from the x-axis, making the graph steeper.

What is the effect of a vertical compression on a function?

A vertical compression decreases the distance of points from the x-axis, making the graph flatter.

What does a horizontal stretch do to a function?

A horizontal stretch increases the distance of points from the y-axis, making the graph wider.

What does a horizontal compression do to a function?

A horizontal compression decreases the distance of points from the y-axis, making the graph narrower.

What is the general form of a transformed quadratic function?

The general form is $$g(x) = a(x - h)^2 + k$$ , where (h, k) is the vertex and 'a' determines the direction and width of the parabola.

12.16.24 A2 Transformation of Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a transformation of a function?

Back

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

2.

FLASHCARD QUESTION

Front

What does a horizontal translation of a function do?

Back

A horizontal translation shifts the graph of the function left or right along the x-axis.

3.

FLASHCARD QUESTION

Front

What does a vertical translation of a function do?

Back

A vertical translation shifts the graph of the function up or down along the y-axis.

4.

FLASHCARD QUESTION

Front

Back

The function shifts left 3 units and down 12 units.

5.

FLASHCARD QUESTION

Front

Back

The function shifts left 4 units and down 9 units.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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