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# Precalculus Formulas Flashcards

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@WellBlue

### What is the Slope-Intercept Form?

• I = Prt
• y-y1=m(x-x1)
• d = rt
• y = mx + b (correct)
• ### What is the Slope-Point Form?

y - y1 = m(x - x1)

### What is the Slope Formula?

(y₂ - y₁) / (x₂ - x₁)

### What does L₁ | L₂ represent?

<p>m₁ = -1 / m₂</p> Signup and view all the answers

### What is the Speed-Time-Distance formula?

<p>d = rt</p> Signup and view all the answers

### What is the formula for Simple Interest?

<p>I = Prt</p> Signup and view all the answers

### What is the formula for Compounded Interest?

<p>A = P(1 + r/n)^(nt)</p> Signup and view all the answers

### What is the Carbon-14 Decay Rate?

<p>-0.00012</p> Signup and view all the answers

### What is the formula for Interest Compounded Continuously?

<p>A = Pe^(rt)</p> Signup and view all the answers

### What is the Half-Life Formula?

<p>1/2 = e^(rt)</p> Signup and view all the answers

### What is the Doubling Time Formula?

<p>2 = e^(rt)</p> Signup and view all the answers

### What is the Distance Formula?

<p>d = √[(x₂ - x₁)² + (y₂ - y₁)²]</p> Signup and view all the answers

### What is the Midpoint Formula?

<p>(x₁ + x₂)/2, (y₁ + y₂)/2</p> Signup and view all the answers

### What is the Circle Formula?

<p>(x - h)² + (y - k)² = r²</p> Signup and view all the answers

### What is a Complex Number?

<p>a + bi</p> Signup and view all the answers

### What is the Difference Quotient?

<p>(f(x + h) - f(x)) / h</p> Signup and view all the answers

### What is the Quadratic Formula?

<p>[-b ± √(b² - 4ac)] / (2a)</p> Signup and view all the answers

### What is the Direct Variation formula?

<p>y = kx</p> Signup and view all the answers

### What is the Inverse Variation formula?

<p>y = k / x</p> Signup and view all the answers

### What does (f + g)(x) represent?

<p>f(x) + g(x)</p> Signup and view all the answers

### What does (f - g)(x) represent?

<p>f(x) - g(x)</p> Signup and view all the answers

### What does (fg)(x) represent?

<p>f(x) * g(x)</p> Signup and view all the answers

### What does (f / g)(x) represent?

<p>f(x) / g(x)</p> Signup and view all the answers

### What does (f º g)(x) represent?

<p>f(g(x))</p> Signup and view all the answers

### What does y = -f(x) represent?

<p>Reflected across x-axis</p> Signup and view all the answers

### What does y = f(-x) represent?

<p>Reflected across y-axis</p> Signup and view all the answers

### What is an Even Function?

<p>f(-x) = f(x)</p> Signup and view all the answers

### What is an Odd Function?

<p>f(-x) = -f(x)</p> Signup and view all the answers

### What is Log Form?

<p>log₁₀ x = y</p> Signup and view all the answers

### What is Exponent Form?

<p>10^y = x</p> Signup and view all the answers

### What is the Change of Base Formula?

<p>log₅ M = log₁₀ M / log₁₀ 5</p> Signup and view all the answers

### What is the Determinant of a 2x2 Matrix?

<p>| a d | = ad - bc</p> Signup and view all the answers

## Study Notes

### Linear Equations

• Slope-Intercept Form: Expressed as y = mx + b, where m is the slope and b is the y-intercept.
• Slope-Point Form: Given by y - y₁ = m(x - x₁), representing a linear equation using a point (x₁, y₁) and slope m.
• Slope Formula: Calculated as (y₂ - y₁) / (x₂ - x₁), determines the steepness of a line between two points.

### Line Relationships

• Perpendicular Lines: If two lines L₁ and L₂ are perpendicular, their slopes satisfy m₁ = -1 / m₂.

### Motion and Financial Calculations

• Speed-Time-Distance: d = rt, where d is distance, r is rate, and t is time.
• Simple Interest: Calculated as I = Prt, where I is interest, P is principal, r is rate, and t is time.
• Compounded Interest: A = P(1 + r/n)^(nt) reflects interest added at specified intervals.

### Exponential Decay

• Carbon-14 Decay Rate: Approximately -0.00012, representing the rate of decay for carbon-14 isotopes.
• Continuously Compounded Interest: Utilized with A = Pe^rt, where e is the base of natural logarithms.
• Half-Life Formula: Expressed as 1/2 = e^rt, denotes the time required for half of a substance to decay.
• Doubling Time Formula: Stated as 2 = e^rt, indicates the time required for a quantity to double.

### Geometry and Distance

• Distance Formula: Determined with d = √[(x₂ - x₁)² + (y₂ - y₁)²], representing the distance between two points in a plane.
• Midpoint Formula: Given by (x₁ + x₂/2, y₁ + y₂/2), calculates the midpoint between two points.
• Circle Formula: Represented as (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

### Algebraic Concepts

• Complex Numbers: Formed as a + bi, combining real and imaginary parts.
• Difference Quotient: Calculated as (f(x + h) - f(x)) / h, essential in finding derivatives.

• Quadratic Formula: Solving for x in ax² + bx + c = 0 provides x = [-b ± √(b² - 4ac)] / (2a).

### Variation Relations

• Direct Variation: Expressed as y = kx, indicating a proportional relationship where k is constant.
• Inverse Variation: Written as y = k / x, showing a relationship where y decreases as x increases.

### Function Operations

• Function Addition: (f + g)(x) = f(x) + g(x), combining two functions.
• Function Subtraction: (f - g)(x) = f(x) - g(x), determining the difference between two functions.
• Function Multiplication: (fg)(x) = f(x) * g(x), represents the product of two functions.
• Function Division: (f / g)(x) = f(x) / g(x), portraying the division of two functions.
• Function Composition: (f º g)(x) = f(g(x)), combining two functions by substituting.

### Function Transformations

• Reflection Across X-axis: y = -f(x) indicates a vertical reflection of the function.
• Reflection Across Y-axis: y = f(-x) indicates a horizontal reflection of the function.

### Function Symmetry

• Even Function: Characterized by f(-x) = f(x), symmetrical around the y-axis.
• Odd Function: Identified by f(-x) = -f(x), symmetrical around the origin.

### Logarithmic Functions

• Logarithmic Form: log₁₀ x = y denotes the logarithm of x to the base 10.
• Exponent Form: 10^y = x transforms the logarithmic equation to exponential.
• Change of Base Formula: log₅ M = log₁₀ M / log₁₀ 5 allows conversion between logarithmic bases.

### Matrix Calculations

• Determinant of 2x2 Matrix: Calculated using | a d | | b c | = ad - bc, providing a scalar value representing matrix properties.

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## Description

Test your knowledge of essential precalculus formulas with these flashcards. Covering concepts such as slope-intercept form, slope-point form, and various interest calculations, these cards are a great way to reinforce your understanding. Perfect for students looking to master precalculus concepts quickly and effectively.

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