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Sine

5.1

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Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A particle starts at x = 0 and moves along the x-axis with velocity v(t) = 0.2 for time t ? 0. Where is the particle at t = 7? A) x = 0.2 B) x = 1.4 C) x = 0.27 D) x = 7 1) 2) A particle moves with velocity v(t) = 2t + 7 find the distance traveled between t = 1 and t = 5. A) 18 B) 52 C) 26 D) 9 2) 3) A particle moves with velocity v(t) = 2t + 3 find the distance traveled between t = 0 and t = 2. A) 13 B) 15 C) 10 D) 17 3) Use a finite approximation to estimate the area of the region enclosed between the graph of f and the x-axis for a ? x ? b. 4) f(x) = x2, a = 2, b = 6

Precalculus Functions Anecdotes

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1. Identity Function-This is the only function thats acts on every real number by leaving it alone 2. Square Root Function-Put any positive number into your calculator. Take the square root. Then take the square root again, and so on. Eventually you will always get 1. 3. Squaring Function-The graph of this function, called a parabola, had a reflection property that is useful in making flashlights and satellite dishes. 4. Cubing Function-The origin is called a ?point of inflection? for this curve because the graph changes the curvature at the point. 5. Reciprocal Function-This curve, called a hyperbola, also has a reflection property that is useful in satellite dishes. 6. Natural Log Function-This function increases very slowly. If the x-axis and y-axis

Pre-Calculus Functions Chart

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Sheet1 Formula Name Domain Range Increasing Interval Decreasing Interval Maximum Minimum x-Intercept y-Intercept End-Behavior VA HA Symmetry Continuity 1a(Parent) f(x)=x Identity Function (-?,?) (-?,?) (-?,?) None None None (0,0) (0,0) y-->? None None Odd Continuous 1b f(x)=x-6 None (-?,?) (-?,?) (-?,?) None None None (6,0) (0,-6) y-->? None None Neither Continuous 1c f(x)=x+3 None (-?,?) (-?,?) (-?,?) None None None (-3,0) (0,3) y-->? None None Neither Continuous 1d f(x)=3x None (-?,?) (-?,?) (-?,?) None None None (0,0) (0,0) y-->? None None Neither Continuous 1e f(x)=-x None (-?,?) (-?,?) None (-?,?) None None (0,0) (0,0) y-->-? None None Neither Continuous 1f f(x)=-3x+6 None (-?,?) (-?,?) None (-?,?) None None (2,0) (0,6) y-->-? None None Neither Continuous 1g y=a(x-h) +k

Summary of Trig Inverse Function

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Trig Inverse Function Summary Function Meaning Domain Range Quadrants of Found on the (i.e., possible (i.e., possible the Unit Circle calculator by values for x) values for y) from Which Range Values Come j=sin!x y is the angle in the first or [-1, 1] [-nI2, n12] I and IV sin" (X) j=arcsin x fourth quadrant whose sine value is x j=cosir Y is the angle in the first or [-1, 1] [0, n] I and II cos-I(X) y=arccos x second quadrant whose cosine value is x j=tanix y is the angle in the first or (-00, (0) (-nl2, n12) I and IV tan" (X) y=arctanx fourth quadrant whose , tangent value is x

Trig formula sheet

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All Rights Reserved: http://regentsprep.org Algebra 2 ? Things to Remember! Exponents: 0 1x ? 1m m x x ? ? ?m n m nx x x ?? ?( )n m n mx x? m m n n x x x ?? n n n x x y y ? ? ?? ?? ? ( ) ?n n nxy x y? Complex Numbers: 1 i? ? ; 0a i a a? ? ? 2 1i ? ? 14 2 1i i? ? ? divide exponent by 4, use remainder, solve. ( ) conjugate ( )a bi a bi? ? 2 2( )( )a bi a bi a b? ? ? ? 2 2a bi a b? ? ? absolute value=magnitude Logarithms log yby x x b? ? ? ln logex x? natural log e = 2.71828? 10log logx x? common log Change of base formula: log log logb a a b
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