AP Precalculus Flashcards: Change In Linear And Exponential Functions

Study Change In Linear And Exponential 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

Change In Linear And Exponential Functions

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QUESTION

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What is the effect of a zero slope in a linear function?

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ANSWER

Horizontal line. Zero slope creates constant function value.

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What this deck covers

This deck focuses on Change In Linear And Exponential Functions, giving you a quick way to review the definitions, rules, and examples that matter most for AP Precalculus.

How to use these flashcards

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.

All flashcards

Flashcard 1: What is the effect of a zero slope in a linear function?

Answer: Horizontal line. Zero slope creates constant function value.

Flashcard 2: If $f(x) = 6x - 9$ , what is $f(2)$ ?

Answer:

Substitute $x = 2$ : $f(2) = 6(2) - 9 = 3$ .

Flashcard 3: Find the slope of the line passing through points $(1, 2)$ and $(3, 6)$ .

Answer:

Slope = $\frac{6-2}{3-1} = \frac{4}{2} = 2$ .

Flashcard 4: Find the slope of the line passing through points $(1, 2)$ and $(3, 6)$ .

Answer:

Slope = $\frac{6-2}{3-1} = \frac{4}{2} = 2$ .

Flashcard 5: Find $f(x)$ if $f(x) = 2 \times 3^x$ and $x = 2$ .

Answer:

Substitute $x = 2$ : $f(2) = 2 \times 3^2 = 18$ .

Flashcard 6: What is the formula for an exponential function?

Answer: $f(x) = a \times b^x$ . Where $a$ is initial value and $b$ is the base.

Flashcard 7: Identify the linear function: $f(x) = 2x - 5$ or $f(x) = 3^x$ ?

Answer: $f(x) = 2x - 5$ . Form $mx + b$ indicates linear function.

Flashcard 8: What does a negative exponent in an exponential function represent?

Answer: Reciprocal growth. Negative exponent means division by positive power.

Flashcard 9: Find the rate of change for $f(x) = 5x + 3$ .

Answer: $5$ . The coefficient of $x$ is the rate of change.

Flashcard 10: What is the rate of change in $f(x) = x + 4$ ?

Answer:

The slope is the coefficient of $x$ .

Flashcard 11: Describe the graph of $f(x) = b^x$ when $0 < b < 1$ .

Answer: Decaying exponential. Base less than 1 creates decreasing exponential.

Flashcard 12: What is the general form of a linear function?

Answer: $f(x) = mx + b$ . Standard form with slope $m$ and y-intercept $b$ .

Flashcard 13: Describe the graph of $f(x) = b^x$ when $b > 1$ .

Answer: Growing exponential. Base greater than 1 creates increasing exponential.

Flashcard 14: Find the initial value of $f(x) = 10 \times 0.9^x$ .

Answer:

The coefficient multiplying the exponential term.

Flashcard 15: What is the impact of a negative slope in a linear function?

Answer: Decreasing function. Negative slope means function decreases as $x$ increases.

Flashcard 16: What is the common ratio in $f(x) = 7 \times 3^x$ ?

Answer:

The base of the exponential term.

Flashcard 17: Find the y-intercept of $f(x) = -3x + 12$ .

Answer:

Y-intercept occurs when $x = 0$ .

Flashcard 18: State the decay factor in $f(x) = 5 \times 0.8^x$ .

Answer: 0.8. The base represents decay when between 0 and 1.

Flashcard 19: State the initial value in $f(x) = 4 \times 2^x$ .

Answer:

The coefficient multiplying the exponential term.

Flashcard 20: Identify the y-intercept in the linear function $f(x) = -2x + 5$ .

Answer:

The constant term is the y-intercept.

Flashcard 21: If $f(x) = 4 \times 2^x$ , what is $f(3)$ ?

Answer:

Substitute $x = 3$ : $f(3) = 4 \times 2^3 = 32$ .

Flashcard 22: What is the effect of doubling the coefficient in a linear function?

Answer: Steeper slope. Larger coefficient creates steeper line.

Flashcard 23: What does the y-intercept represent in a linear function?

Answer: Initial value. Y-intercept is the starting value when $x = 0$ .

Flashcard 24: What happens when the exponent in an exponential function is negative?

Answer: Function decreases. Negative exponent creates reciprocal, decreasing function.

Flashcard 25: Find $f(0)$ for $f(x) = 9 \times 2^x$ .

Answer:

At $x = 0$ : $f(0) = 9 \times 2^0 = 9$ .

Flashcard 26: Determine the type: $f(x) = 4 \times 1.5^x$ .

Answer: Exponential function. Form $a \times b^x$ identifies exponential function.

Flashcard 27: Calculate $f(0)$ for $f(x) = 5x - 7$ .

Answer: -7. At $x = 0$ : $f(0) = 5(0) - 7 = -7$ .

Flashcard 28: Identify the growth factor in $f(x) = 2 \times 1.1^x$ .

Answer: 1.1. The base represents growth when greater than 1.

Flashcard 29: Which function type has a constant ratio between outputs?

Answer: Exponential function. Exponential functions have constant multiplicative rate.

Flashcard 30: Identify the exponential function: $f(x) = 5x$ or $f(x) = 2 \times 3^x$ ?

Answer: $f(x) = 2 \times 3^x$ . Form $a \times b^x$ indicates exponential function.

Flashcard 31: Which function type has a constant rate of change?

Answer: Linear function. Linear functions have constant slope.

Flashcard 32: Identify the slope in the linear function $f(x) = 3x + 7$ .

Answer:

The coefficient of $x$ is the slope.

Flashcard 33: What is the y-intercept of $f(x) = 6x - 8$ ?

Answer: -8. The constant term when $x = 0$ .

Flashcard 34: Find $f(4)$ for $f(x) = 7 \times 2^x$ .

Answer:

Substitute $x = 4$ : $f(4) = 7 \times 2^4 = 112$ .

Flashcard 35: Determine the type: $f(x) = 0.5x - 2$ .

Answer: Linear function. Form $mx + b$ identifies linear function.

Flashcard 36: What is the base in the exponential function $f(x) = 3 \times (0.5)^x$ ?

Answer: 0.5. The number being raised to the power.

Flashcard 37: What is the effect of doubling the base in an exponential function?

Answer: Increases the growth rate. Larger base means faster exponential growth.

Flashcard 38: What does the slope represent in a linear function?

Answer: Rate of change. Slope shows how much $y$ changes per unit of $x$ .

Flashcard 39: Calculate $f(1)$ for $f(x) = 3 \times (0.5)^x$ .

Answer: 1.5. At $x = 1$ : $f(1) = 3 \times (0.5)^1 = 1.5$ .

AP Precalculus Flashcards: Change In Linear And Exponential Functions

Change In Linear And Exponential Functions

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: What is the effect of a zero slope in a linear function?

Flashcard 2: If f(x)=6x−9f(x) = 6x - 9f(x)=6x−9, what is f(2)f(2)f(2)?

Flashcard 3: Find the slope of the line passing through points (1,2)(1, 2)(1,2) and (3,6)(3, 6)(3,6).

Flashcard 4: Find the slope of the line passing through points (1,2)(1, 2)(1,2) and (3,6)(3, 6)(3,6).

Flashcard 5: Find f(x)f(x)f(x) if f(x)=2×3xf(x) = 2 \times 3^xf(x)=2×3x and x=2x = 2x=2.

Flashcard 6: What is the formula for an exponential function?

Flashcard 7: Identify the linear function: f(x)=2x−5f(x) = 2x - 5f(x)=2x−5 or f(x)=3xf(x) = 3^xf(x)=3x?

Flashcard 8: What does a negative exponent in an exponential function represent?

Flashcard 9: Find the rate of change for f(x)=5x+3f(x) = 5x + 3f(x)=5x+3.

Flashcard 10: What is the rate of change in f(x)=x+4f(x) = x + 4f(x)=x+4?

Flashcard 11: Describe the graph of f(x)=bxf(x) = b^xf(x)=bx when 0<b<10 < b < 10<b<1.

Flashcard 12: What is the general form of a linear function?

Flashcard 13: Describe the graph of f(x)=bxf(x) = b^xf(x)=bx when b>1b > 1b>1.

Flashcard 14: Find the initial value of f(x)=10×0.9xf(x) = 10 \times 0.9^xf(x)=10×0.9x.

Flashcard 15: What is the impact of a negative slope in a linear function?

Flashcard 16: What is the common ratio in f(x)=7×3xf(x) = 7 \times 3^xf(x)=7×3x?

Flashcard 17: Find the y-intercept of f(x)=−3x+12f(x) = -3x + 12f(x)=−3x+12.

Flashcard 18: State the decay factor in f(x)=5×0.8xf(x) = 5 \times 0.8^xf(x)=5×0.8x.

Flashcard 19: State the initial value in f(x)=4×2xf(x) = 4 \times 2^xf(x)=4×2x.

Flashcard 20: Identify the y-intercept in the linear function f(x)=−2x+5f(x) = -2x + 5f(x)=−2x+5.

Flashcard 21: If f(x)=4×2xf(x) = 4 \times 2^xf(x)=4×2x, what is f(3)f(3)f(3)?

Flashcard 22: What is the effect of doubling the coefficient in a linear function?

Flashcard 23: What does the y-intercept represent in a linear function?

Flashcard 24: What happens when the exponent in an exponential function is negative?

Flashcard 25: Find f(0)f(0)f(0) for f(x)=9×2xf(x) = 9 \times 2^xf(x)=9×2x.

Flashcard 26: Determine the type: f(x)=4×1.5xf(x) = 4 \times 1.5^xf(x)=4×1.5x.

Flashcard 27: Calculate f(0)f(0)f(0) for f(x)=5x−7f(x) = 5x - 7f(x)=5x−7.

Flashcard 28: Identify the growth factor in f(x)=2×1.1xf(x) = 2 \times 1.1^xf(x)=2×1.1x.

Flashcard 29: Which function type has a constant ratio between outputs?

Flashcard 30: Identify the exponential function: f(x)=5xf(x) = 5xf(x)=5x or f(x)=2×3xf(x) = 2 \times 3^xf(x)=2×3x?

Flashcard 31: Which function type has a constant rate of change?

Flashcard 32: Identify the slope in the linear function f(x)=3x+7f(x) = 3x + 7f(x)=3x+7.

Flashcard 33: What is the y-intercept of f(x)=6x−8f(x) = 6x - 8f(x)=6x−8?

Flashcard 34: Find f(4)f(4)f(4) for f(x)=7×2xf(x) = 7 \times 2^xf(x)=7×2x.

Flashcard 35: Determine the type: f(x)=0.5x−2f(x) = 0.5x - 2f(x)=0.5x−2.

Flashcard 36: What is the base in the exponential function f(x)=3×(0.5)xf(x) = 3 \times (0.5)^xf(x)=3×(0.5)x?

Flashcard 37: What is the effect of doubling the base in an exponential function?

Flashcard 38: What does the slope represent in a linear function?

Flashcard 39: Calculate f(1)f(1)f(1) for f(x)=3×(0.5)xf(x) = 3 \times (0.5)^xf(x)=3×(0.5)x.

Flashcard 2: If $f(x) = 6x - 9$ , what is $f(2)$ ?

Flashcard 3: Find the slope of the line passing through points $(1, 2)$ and $(3, 6)$ .

Flashcard 4: Find the slope of the line passing through points $(1, 2)$ and $(3, 6)$ .

Flashcard 5: Find $f(x)$ if $f(x) = 2 \times 3^x$ and $x = 2$ .

Flashcard 7: Identify the linear function: $f(x) = 2x - 5$ or $f(x) = 3^x$ ?

Flashcard 9: Find the rate of change for $f(x) = 5x + 3$ .

Flashcard 10: What is the rate of change in $f(x) = x + 4$ ?

Flashcard 11: Describe the graph of $f(x) = b^x$ when $0 < b < 1$ .

Flashcard 13: Describe the graph of $f(x) = b^x$ when $b > 1$ .

Flashcard 14: Find the initial value of $f(x) = 10 \times 0.9^x$ .

Flashcard 16: What is the common ratio in $f(x) = 7 \times 3^x$ ?

Flashcard 17: Find the y-intercept of $f(x) = -3x + 12$ .

Flashcard 18: State the decay factor in $f(x) = 5 \times 0.8^x$ .

Flashcard 19: State the initial value in $f(x) = 4 \times 2^x$ .

Flashcard 20: Identify the y-intercept in the linear function $f(x) = -2x + 5$ .

Flashcard 21: If $f(x) = 4 \times 2^x$ , what is $f(3)$ ?

Flashcard 25: Find $f(0)$ for $f(x) = 9 \times 2^x$ .

Flashcard 26: Determine the type: $f(x) = 4 \times 1.5^x$ .

Flashcard 27: Calculate $f(0)$ for $f(x) = 5x - 7$ .

Flashcard 28: Identify the growth factor in $f(x) = 2 \times 1.1^x$ .

Flashcard 30: Identify the exponential function: $f(x) = 5x$ or $f(x) = 2 \times 3^x$ ?

Flashcard 32: Identify the slope in the linear function $f(x) = 3x + 7$ .

Flashcard 33: What is the y-intercept of $f(x) = 6x - 8$ ?

Flashcard 34: Find $f(4)$ for $f(x) = 7 \times 2^x$ .

Flashcard 35: Determine the type: $f(x) = 0.5x - 2$ .

Flashcard 36: What is the base in the exponential function $f(x) = 3 \times (0.5)^x$ ?

Flashcard 39: Calculate $f(1)$ for $f(x) = 3 \times (0.5)^x$ .