Algebra ll C final exam flash cards

Help study and memorize items used on final exam

What are the steps to find the inverse of a function?

1. Replace f(x) with y 2. Swap x and y 3. Solve for y 4. Rename y as f⁻¹(x)

Find the inverse of f(x) = 2x + 3

f⁻¹(x) = (x – 3)/2

What is the product property of logarithms?

logₐ(xy) = logₐ(x) + logₐ(y)

What is the quotient property of logarithms?

logₐ(x/y) = logₐ(x) – logₐ(y)

What is the power property of logarithms?

logₐ(xⁿ) = n·logₐ(x)

What is the change of base formula?

logₐ(x) = log(x) / log(a)

How do you solve logarithmic or exponential equations?

Use properties, isolate the log or exponent, convert using log_b(x) = y ⇔ b^y = x

What are the radian equivalents of 0°, 30°, 45°, 60°, and 90°?

0 = 0, 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2

What are the coordinates for π/6, π/4, and π/3 on the unit circle?

π/6 = (√3/2, 1/2), π/4 = (√2/2, √2/2), π/3 = (1/2, √3/2)

What is the general form of a sine or cosine graph?

y = A·sin(Bx + C) + D

What do A, B, C, and D represent in the trig graph equation?

A = amplitude, B = affects period (2π/B), C = phase shift, D = vertical shift

What does SOH-CAH-TOA stand for?

sin = opp/hyp, cos = adj/hyp, tan = opp/adj

How do you find an angle using inverse trig functions?

θ = sin⁻¹(opposite/hypotenuse), or use cos⁻¹ or tan⁻¹ similarly

What is the quadratic formula?

x = [-b ± √(b² – 4ac)] / 2a

What happens if b² – 4ac < 0?

The solution is complex (involves imaginary numbers)

What is i and i²?

i = √–1, i² = –1

How do you add/subtract complex numbers?

(a + bi) ± (c + di) = (a±c) + (b±d)i

How do you multiply complex numbers?

Use FOIL, then simplify using i² = –1

How does the degree of a polynomial affect the graph?

Degree = number of roots (maximum)

What’s the end behavior of even vs. odd degree polynomials?

Even: both ends same; Odd: ends opposite

How do you write a polynomial from its zeros 2, –1, 3?

f(x) = a(x–2)(x+1)(x–3)

What are the methods for solving systems of equations?

Substitution and elimination

What are the possible types of solutions for systems?

One solution, no solution, or infinite solutions

Define mean, median, mode, and range

Mean = average; Median = middle; Mode = most frequent; Range = max – min

What is the vertex form of a quadratic?

y = a(x – h)² + k, where (h, k) is the vertex

How do you convert standard form to vertex form?

By completing the square