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Questions and Answers
What is the vertex of the hyperbola 25x^2 - 100y^2 = 1?
What is the vertex of the hyperbola 25x^2 - 100y^2 = 1?
- (10, 0)
- (0, 0) (correct)
- (0, 5)
- (5, 0)
What is the value of cot(π/3)?
What is the value of cot(π/3)?
- 1/√3 (correct)
- 3
- 1/3
- √3
What is the value of sin(𝛼 + 𝛽) if sin 𝛼 = 5/13 and cos 𝛽 = 12/13?
What is the value of sin(𝛼 + 𝛽) if sin 𝛼 = 5/13 and cos 𝛽 = 12/13?
- 5/13 (correct)
- 12/13
- 1
- -1
What is the domain of f(x) = log₉(x - 6)?
What is the domain of f(x) = log₉(x - 6)?
What is the equation of the graph of f(x) = -x^2(x - 1)(x + 3)?
What is the equation of the graph of f(x) = -x^2(x - 1)(x + 3)?
What is the amplitude of the function y = 2cos(2x + π)?
What is the amplitude of the function y = 2cos(2x + π)?
What is the value of sin²(x) + cos²(x) cot²(x)?
What is the value of sin²(x) + cos²(x) cot²(x)?
What is the phase shift of the function y = -2sin(4x - π)?
What is the phase shift of the function y = -2sin(4x - π)?
What is the inverse of the function f(x) = (7x + 6) / (x - 5)?
What is the inverse of the function f(x) = (7x + 6) / (x - 5)?
What is the value of log₇√(x⁵y / 49) simplified?
What is the value of log₇√(x⁵y / 49) simplified?
What is the period of the function y = 2cos(2x + 4)?
What is the period of the function y = 2cos(2x + 4)?
What is the value of cos(θ) given tan(θ) = -3 and θ in quadrant 2?
What is the value of cos(θ) given tan(θ) = -3 and θ in quadrant 2?
What is the value of tan(π)?
What is the value of tan(π)?
What is the value of cos(3π/2)?
What is the value of cos(3π/2)?
What is the horizontal asymptote of h(x) = (10x³) / (2x² + 1)?
What is the horizontal asymptote of h(x) = (10x³) / (2x² + 1)?
What is the general term of the arithmetic sequence with a1 = -19 and d = 7?
What is the general term of the arithmetic sequence with a1 = -19 and d = 7?
What is the value of the expression 5log₇(4) + log₇(r - 8) - log₇r?
What is the value of the expression 5log₇(4) + log₇(r - 8) - log₇r?
What is the measure of the angle between the end of the shadow and the vertical side of the building?
What is the measure of the angle between the end of the shadow and the vertical side of the building?
What is the inverse of the one-to-one function f(x) = (2x + 2) / (x - 2)?
What is the inverse of the one-to-one function f(x) = (2x + 2) / (x - 2)?
What is the domain of the function f(x) = x³ - 36x?
What is the domain of the function f(x) = x³ - 36x?
What is the value of (g ∘ f)(-3)?
What is the value of (g ∘ f)(-3)?
What is the domain of the function g(x) = x² - 9 / (x + 2)?
What is the domain of the function g(x) = x² - 9 / (x + 2)?
What is the length of the guy wire that makes an angle of 20° with the ground?
What is the length of the guy wire that makes an angle of 20° with the ground?
What is the exact value of tan⁻¹(√3)?
What is the exact value of tan⁻¹(√3)?
What is the value of (f ◦ g)(1) using the graphs of f and g?
What is the value of (f ◦ g)(1) using the graphs of f and g?
What is the solution to the logarithmic equation log 4 (x − 4) + log 4(x − 10) = 2?
What is the solution to the logarithmic equation log 4 (x − 4) + log 4(x − 10) = 2?
What is the domain of the function g(x) = √(x-9)/√(x-1)?
What is the domain of the function g(x) = √(x-9)/√(x-1)?
What is the exact value of sin⁻¹(√2/2)?
What is the exact value of sin⁻¹(√2/2)?
What is the value of f(-1) for the given piecewise function?
What is the value of f(-1) for the given piecewise function?
What is the polynomial with zeros -8, 1 (multiplicity 2), and degree 3?
What is the polynomial with zeros -8, 1 (multiplicity 2), and degree 3?
What is the exact value of sec(−3π/4)?
What is the exact value of sec(−3π/4)?
What is the domain of the function f(x) = √(14-x)/x²?
What is the domain of the function f(x) = √(14-x)/x²?
What is the solution of the equation 5𝑥 + 6 / 22𝑥 - 7?
What is the solution of the equation 5𝑥 + 6 / 22𝑥 - 7?
What is the inverse of 𝑓(𝑥) = 3𝑥 - 2?
What is the inverse of 𝑓(𝑥) = 3𝑥 - 2?
What is the value of 𝜃 if 𝜃 = tan^(-1) (13/5)?
What is the value of 𝜃 if 𝜃 = tan^(-1) (13/5)?
What is the range of the function 𝑓(𝑥) = |𝑥| - 3?
What is the range of the function 𝑓(𝑥) = |𝑥| - 3?
What is the amplitude, period, and phase shift of the function 𝑓(𝑥) = 2sin(𝑥 + 𝜋/8)?
What is the amplitude, period, and phase shift of the function 𝑓(𝑥) = 2sin(𝑥 + 𝜋/8)?
What is the value of 𝑎𝑛 in the sequence 𝑎𝑛 = 7𝑛 - 26?
What is the value of 𝑎𝑛 in the sequence 𝑎𝑛 = 7𝑛 - 26?
What is the domain of the function 𝑓(𝑥) = 1 / (𝑥 - 3)?
What is the domain of the function 𝑓(𝑥) = 1 / (𝑥 - 3)?
What is the 𝑥-intercept of the function 𝑓(𝑥) = 𝑥^4 - 3𝑥^3 + 2𝑥^2 - 12𝑥?
What is the 𝑥-intercept of the function 𝑓(𝑥) = 𝑥^4 - 3𝑥^3 + 2𝑥^2 - 12𝑥?
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Study Notes
Composite Functions
- Evaluate composite functions using graphs, e.g., (f ◦ g)(1)
Logarithmic Equations
- Solve logarithmic equations, e.g., log 4 (x − 4) + log 4 (x − 10) = 2
- Reject any value not in the domain of the original logarithmic expressions
Function Domain
- Find the domain of functions, e.g., g(x) = √(x−9)
- Domain may be a union of intervals, e.g., (1, 9) ∪ (9, ∞)
Trigonometry
- Solve triangles, e.g., 7, 30°, and 115°
- Evaluate trig functions, e.g., sin−1 (2)
- Use reference angles to find exact values, e.g., sec (4π/3)
Polynomials
- Form a polynomial with given zeros and degree, e.g., (x + 8)(x - 1)^2
Piecewise Functions
- Evaluate piecewise functions, e.g., f(-1)
- Graph piecewise functions, e.g., f(x) = {4x - 3 if x < -1, -2x + 4 if x ≥ -1}
Inverse Functions
- Find the inverse of a one-to-one function, e.g., f(x) = x/(x - 5)
- Evaluate inverse functions, e.g., f(-2), f(0), f(2)
Logarithmic Expressions
- Expand logarithmic expressions using properties of logarithms, e.g., log 7 (√(x^5 y) / 49)
- Evaluate logarithmic expressions, e.g., log (x + 30) - log (3) = log (2x + 1)
Function Operations
- Evaluate the difference quotient for a function, e.g., f(x) = x^2 + 9x - 2
Graphing
- Graph functions, e.g., 4x^2 = 64 - 16y^2
- Identify vertices, foci, and asymptotes of conic sections, e.g., ellipse
- Analyze graphs of functions, e.g., f(x) = -x^2 (x - 1)(x + 3)
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