What is the effect of multiplying a function by a factor greater than 1, like $$f(x) = 2|x|$$ ?

It vertically stretches the graph.

What is the effect of multiplying a function by a factor between 0 and 1, like $$f(x) = 0.5|x|$$ ?

It vertically compresses the graph.

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

The graph shifts right 1 unit and up 3 units.

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

The graph reflects across the x-axis and shifts up 1 unit.

Parent Functions and Transformations Flashcards: 15 Cards

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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 in a family of functions, representing the basic shape of the graph.

2.

FLASHCARD QUESTION

Front

What does a horizontal transformation do to a function?

Back

A horizontal transformation moves the graph left or right.

3.

FLASHCARD QUESTION

Front

What does a vertical transformation do to a function?

Back

A vertical transformation moves the graph up or down.

4.

FLASHCARD QUESTION

Front

What is the parent function of a linear function?

Back

The parent function of a linear function is $f(x) = x$ .

5.

FLASHCARD QUESTION

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is $f(x) = x^2$ .

6.

FLASHCARD QUESTION

Front

What is the parent function of an absolute value function?

Back

The parent function of an absolute value function is $f(x) = |x|$ .

7.

FLASHCARD QUESTION

Front

How does the graph of $f(x) = |x - 3|$ transform?

Back

The graph shifts right 3 units.

8.

FLASHCARD QUESTION

Front

How does the graph of $f(x) = |x| + 2$ transform?

Back

The graph shifts up 2 units.

9.

FLASHCARD QUESTION

Front

What effect does a negative sign have in front of a function, like $f(x) = -|x|$ ?

Back

It reflects the graph across the x-axis.

10.

FLASHCARD QUESTION

Front

What is the transformation of $f(x) = (x + 4)^2$ ?

Back

The graph shifts left 4 units.

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