AP Precalculus Flashcards: Transformations Of Functions

Study Transformations Of Functions in AP Precalculus with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

AP Precalculus

Transformations Of Functions

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QUESTION

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Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{-x}$

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ANSWER

Reflection across the y-axis. Negative input creates horizontal reflection.

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What this deck covers

This deck focuses on Transformations Of Functions, giving you a quick way to review the definitions, rules, and examples that matter most for AP Precalculus.

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Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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Flashcard 1: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{-x}$

Answer: Reflection across the y-axis. Negative input creates horizontal reflection.

Flashcard 2: What is the effect of $cf(x)$ where $0 < c < 1$ ?

Answer: Vertical compression by a factor of $c$ . Multiplying by factor less than 1 compresses vertically.

Flashcard 3: What is the effect of $f(x)$ to $f(x + c)$ on its domain?

Answer: Subtract $c$ from each element of the domain. Horizontal shift adjusts input values by constant.

Flashcard 4: Identify the transformation: $f(x) = e^x$ to $f(x) = e^{-x}$

Answer: Reflection across the y-axis. Negative exponent reflects exponential across $y$ -axis.

Flashcard 5: What transformation does $-f(x)$ represent?

Answer: Reflection across the x-axis. Negative sign flips graph over the horizontal axis.

Flashcard 6: What is the effect of $cf(x)$ where $c > 1$ ?

Answer: Vertical stretch by a factor of $c$ . Multiplying by factor greater than 1 stretches vertically.

Flashcard 7: Identify the transformation: $f(x) = x^3$ to $f(x) = x^3 - 2$

Answer: Vertical shift downward by 2 units. Subtracting 2 from output moves graph down.

Flashcard 8: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} + 1$

Answer: Vertical shift upward by 1 unit. Adding 1 to function output shifts graph upward.

Flashcard 9: What transformation is applied: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{(x-4)}$ ?

Answer: Horizontal shift right by 4 units. Subtracting 4 from input shifts right by 4.

Flashcard 10: What is the effect of $f(x - c)$ on the graph of $f(x)$ ?

Answer: Horizontal shift right by $c$ units. Subtracting from input moves graph in same direction horizontally.

Flashcard 11: What is the effect of $f(x)$ to $f(-x)$ on its domain?

Answer: Negate each element of the domain. Reflection changes signs of all input values.

Flashcard 12: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} + 7$

Answer: Vertical shift upward by 7 units. Adding 7 to function output shifts upward.

Flashcard 13: What is the effect of $f(x) - c$ on the graph of $f(x)$ ?

Answer: Vertical shift downward by $c$ units. Subtracting constant from function output moves graph down.

Flashcard 14: What transformation does $f(-x)$ represent?

Answer: Reflection across the y-axis. Negative input creates mirror image across vertical axis.

Flashcard 15: Identify the transformation: $f(x) = x^2$ to $f(x) = x^2 + 5$

Answer: Vertical shift upward by 5 units. Adding 5 to function output shifts graph upward.

Flashcard 16: What transformation does $f(x) = x^2$ to $f(x) = -x^2$ represent?

Answer: Reflection across the x-axis. Negative sign flips parabola across $x$ -axis.

Flashcard 17: Identify the transformation: $f(x) = |x|$ to $f(x) = 3|x|$

Answer: Vertical stretch by a factor of 3. Factor 3 multiplies all $y$ -values by 3.

Flashcard 18: What is the effect of $f(x)$ to $-f(x)$ on its range?

Answer: Negate each element of the range. Reflection flips signs of all output values.

Flashcard 19: What transformation does $f(x) = x^2$ to $f(x) = (x + 5)^2$ represent?

Answer: Horizontal shift left by 5 units. Adding 5 to input shifts left by 5 units.

Flashcard 20: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} - 5$

Answer: Vertical shift downward by 5 units. Subtracting 5 from output moves graph downward.

Flashcard 21: Identify the transformation: $f(x) = x^2$ to $f(x) = (x - 3)^2$

Answer: Horizontal shift right by 3 units. Inside parentheses: subtract 3 from $x$ shifts right.

Flashcard 22: What is the effect of $f(x)$ to $cf(x)$ where $c < 0$ ?

Answer: Vertical stretch/compression and reflection across x-axis. Negative coefficient reflects and scales vertically.

Flashcard 23: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} - 3$

Answer: Vertical shift downward by 3 units. Subtracting 3 from function output shifts downward.

Flashcard 24: Identify the transformation: $f(x) = x^3$ to $f(x) = (x + 4)^3$

Answer: Horizontal shift left by 4 units. Adding 4 to input moves graph left by 4.

Flashcard 25: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x+2}$

Answer: Horizontal shift left by 2 units. Adding 2 to input shifts graph left by 2.

Flashcard 26: What is the effect of $f(x + c)$ on the graph of $f(x)$ ?

Answer: Horizontal shift left by $c$ units. Adding to input moves graph opposite direction horizontally.

Flashcard 27: What transformation does $f(x) = x^2$ to $f(x) = (x - 6)^2$ represent?

Answer: Horizontal shift right by 6 units. Subtracting 6 from input shifts right by 6.

Flashcard 28: Identify the transformation: $f(x) = |x|$ to $f(x) = |x - 1|$

Answer: Horizontal shift right by 1 unit. Subtracting 1 from input shifts right by 1.

Flashcard 29: Identify the transformation: $f(x) = |x|$ to $f(x) = |x + 2|$

Answer: Horizontal shift left by 2 units. Adding 2 to input shifts left by 2 units.

Flashcard 30: What is the effect of $f(cx)$ where $0 < c < 1$ ?

Answer: Horizontal stretch by a factor of $\frac{1}{c}$ . Input coefficient less than 1 stretches horizontally.

Flashcard 31: What is the effect of $f(x)$ to $f(x) + c$ on its range?

Answer: Add $c$ to each element of the range. Vertical shift adds constant to all output values.

Flashcard 32: What is the effect of $f(x) + c$ on the graph of $f(x)$ ?

Answer: Vertical shift upward by $c$ units. Adding constant to function output moves graph up.

Flashcard 33: Identify the transformation: $f(x) = |x|$ to $f(x) = 2|x|$

Answer: Vertical stretch by a factor of 2. Coefficient 2 multiplies all $y$ -values by 2.

Flashcard 34: What is the combined effect of $-f(x + 2)$ ?

Answer: Reflection across x-axis and left shift by 2. Combines vertical reflection and horizontal translation.

Flashcard 35: Identify the transformation of $f(x) = x^2$ to $f(x) = 2x^2 + 3$ .

Answer: Vertical stretch by 2 and shift up by 3. Multiplies output by 2, then adds 3 to result.

Flashcard 36: What is the effect of $f(cx)$ where $c > 1$ ?

Answer: Horizontal compression by a factor of $\frac{1}{c}$ . Input coefficient greater than 1 compresses horizontally.

AP Precalculus Flashcards: Transformations Of Functions

Transformations Of Functions

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1−xf(x) = \frac{1}{-x}f(x)=−x1​

Flashcard 2: What is the effect of cf(x)cf(x)cf(x) where 0<c<10 < c < 10<c<1?

Flashcard 3: What is the effect of f(x)f(x)f(x) to f(x+c)f(x + c)f(x+c) on its domain?

Flashcard 4: Identify the transformation: f(x)=exf(x) = e^xf(x)=ex to f(x)=e−xf(x) = e^{-x}f(x)=e−x

Flashcard 5: What transformation does −f(x)-f(x)−f(x) represent?

Flashcard 6: What is the effect of cf(x)cf(x)cf(x) where c>1c > 1c>1?

Flashcard 7: Identify the transformation: f(x)=x3f(x) = x^3f(x)=x3 to f(x)=x3−2f(x) = x^3 - 2f(x)=x3−2

Flashcard 8: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x+1f(x) = \frac{1}{x} + 1f(x)=x1​+1

Flashcard 9: What transformation is applied: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1(x−4)f(x) = \frac{1}{(x-4)}f(x)=(x−4)1​?

Flashcard 10: What is the effect of f(x−c)f(x - c)f(x−c) on the graph of f(x)f(x)f(x)?

Flashcard 11: What is the effect of f(x)f(x)f(x) to f(−x)f(-x)f(−x) on its domain?

Flashcard 12: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x+7f(x) = \frac{1}{x} + 7f(x)=x1​+7

Flashcard 13: What is the effect of f(x)−cf(x) - cf(x)−c on the graph of f(x)f(x)f(x)?

Flashcard 14: What transformation does f(−x)f(-x)f(−x) represent?

Flashcard 15: Identify the transformation: f(x)=x2f(x) = x^2f(x)=x2 to f(x)=x2+5f(x) = x^2 + 5f(x)=x2+5

Flashcard 16: What transformation does f(x)=x2f(x) = x^2f(x)=x2 to f(x)=−x2f(x) = -x^2f(x)=−x2 represent?

Flashcard 17: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=3∣x∣f(x) = 3|x|f(x)=3∣x∣

Flashcard 18: What is the effect of f(x)f(x)f(x) to −f(x)-f(x)−f(x) on its range?

Flashcard 19: What transformation does f(x)=x2f(x) = x^2f(x)=x2 to f(x)=(x+5)2f(x) = (x + 5)^2f(x)=(x+5)2 represent?

Flashcard 20: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x−5f(x) = \frac{1}{x} - 5f(x)=x1​−5

Flashcard 21: Identify the transformation: f(x)=x2f(x) = x^2f(x)=x2 to f(x)=(x−3)2f(x) = (x - 3)^2f(x)=(x−3)2

Flashcard 22: What is the effect of f(x)f(x)f(x) to cf(x)cf(x)cf(x) where c<0c < 0c<0?

Flashcard 23: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x−3f(x) = \frac{1}{x} - 3f(x)=x1​−3

Flashcard 24: Identify the transformation: f(x)=x3f(x) = x^3f(x)=x3 to f(x)=(x+4)3f(x) = (x + 4)^3f(x)=(x+4)3

Flashcard 25: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x+2f(x) = \frac{1}{x+2}f(x)=x+21​

Flashcard 26: What is the effect of f(x+c)f(x + c)f(x+c) on the graph of f(x)f(x)f(x)?

Flashcard 27: What transformation does f(x)=x2f(x) = x^2f(x)=x2 to f(x)=(x−6)2f(x) = (x - 6)^2f(x)=(x−6)2 represent?

Flashcard 28: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=∣x−1∣f(x) = |x - 1|f(x)=∣x−1∣

Flashcard 29: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=∣x+2∣f(x) = |x + 2|f(x)=∣x+2∣

Flashcard 30: What is the effect of f(cx)f(cx)f(cx) where 0<c<10 < c < 10<c<1?

Flashcard 31: What is the effect of f(x)f(x)f(x) to f(x)+cf(x) + cf(x)+c on its range?

Flashcard 32: What is the effect of f(x)+cf(x) + cf(x)+c on the graph of f(x)f(x)f(x)?

Flashcard 33: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=2∣x∣f(x) = 2|x|f(x)=2∣x∣

Flashcard 34: What is the combined effect of −f(x+2)-f(x + 2)−f(x+2)?

Flashcard 35: Identify the transformation of f(x)=x2f(x) = x^2f(x)=x2 to f(x)=2x2+3f(x) = 2x^2 + 3f(x)=2x2+3.

Flashcard 36: What is the effect of f(cx)f(cx)f(cx) where c>1c > 1c>1?