Number Patterns & Equations and Inequalities
Functions and Graphs
Trigonometry
Trigonometric Graphs
Solving Trig Equations
100
The domain of the function g given by √(t-2)/(t-3).
What is D: x≥2, x≠3?
100
(f-g)(x) if f(x) = 3x + 2 and g(x) = 2x - 7.
What is x + 9?
100
-120° in radians.
What is -2π/3?
100
The graph of f(x) = -3 sin (2x) + 1 has an amplitude of this number.
What is 3?
100
The solution to tan x + 5 sin x = 1. (Use your graphing calculator to solve).
What is x = 0.1671 + 2πk, 1.8256 + 2πk, 2.8867 + 2πk, 4.5453 + 2πk?
200
The value of f(-2) if x - 15, x < 0 f(x) = 2x + 20 x ≥ 0
What is f(-2) = -17?
200
The vertex, y-intercepts, and x-intercepts (if any) of the function f(x) = -x^2 - 2x - 7.
What is vertex of (-1, -6), y-int of -7, no x-int?
200
cos x if tan x = 7/4. NO CALCULATOR and rationalize!
What is (4√65)/65?
200
A sine graph that has been reflected over the x-axis, has an amplitude of 2, and a period of pi has this equation.
What is f(x) = -2 sin 2x?
200
The range of the arccosine function; the range of the arcsine function.
What is 0≤y≤2π for arccosine and -π/2≤y≤π/2 for arcsine?
300
The explicit formula for a geometric sequence with first two terms of 2 and -2/5.
What is u_n=2(-1/5)^(n-1)?
300
The inverse relation of f(x) = 1 - x^2 and whether or not it's a function.
What is y = ±√(1-x), which is NOT a function by the HLT?
300
The simplification of (sin x cos x)/(1-cos(sq)x) using trig identities.
What is cot x?
300
The range and domain of the tangent function.
What is a range of all reals and a domain of x≠±π/2 + πk?
300
arctan 1. (NO CALC)
What is π/4?
400
The solution to the inequality (3x+1)/(2x-4)>0 in interval notation.
What is (-∞, -1/3)U(2,∞)?
400
The local maximum and minimum of the function g(x) = x^3 + 8x^2 + 4x - 3 and approximate inflection point.
What is a maximum at x = -5.0704 and a minimum at x = -0.2630 and inflection point of approximately 8/3 or 2.67?
400
If the terminal side of an angle of t radians in standard position passes through the point (-2,3), then tan t equals this number.
What is -3/2?
400
The values of t on the interval [-2π, 2π] for which cos 0.
What is -3π/2, -π/2, π/2, 3π/2?
400
The exact value of cos(arctan √5/2). NO CALC
What is 2/3?
500
The exact solution(s) to √(x+1)+ √(x-1)=1.
What is no solutions?
500
The values of f(0) and f(-3/2) if f(x) = x + |x| + [x]. (Two answers! [x] is the greatest integer function).
What is f(0) = 0 and f(-3/2) = -2?
500
If sin(-101π/2) = -1, then sin(-105π/2) equals this number.
What is -1?
500
The amplitude, period, phase shift and vertical shift of f(x) = 1/2 cos(2t - π) + 3.
What is an amplitude of 1/2, period of π, phase shift of π/2 (right π/2) and vertical shift of +3 (up 3)?
500
All solutions to sin 2x = √2/2. NO CALC
What is π/8 + πk and 3π/8 + πk?
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