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Is the graph a function or a relation? Function Relation

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State the domain of the function: All real numbers except 1 or -1 All real numbers except 3 or -3 All real numbers except 5 All real numbers except 0 and 5

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Find the composition functions below:

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Find the x- and y- intercepts: (12,0) and (0,6)(6,0) and (0,-4)

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Find the zero of each function:

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Dominic is opening a bank. He determined that he will need $22,000 to buy a building and supplies to start. He expects expenses for each following month to be $12,300. Write an equation that models the total expense y after x months.

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Determine whether the graphs of the pair of equations are parallel, coinciding, or neither. x – 2y = 12 and 4x + y = 203x – 2y = -6 and 6x – 4y = -12 NeitherCoinciding

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Write an equation of the line that passes through the points given: (-2,4) and (6,-4)(3,-5) and (0,4)

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Write an equation of a line using the information given. 1. No slope, (3,4)2. slope = 3, (-3, -7) Slope is undefined VERTICAL LINE

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How can you tell if two lines are perpendicular? Their slopes are opposite reciprocals HOW CAN WE TELL IF THEY ARE PARALLEL? Their slopes are the SAME

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Given f(x) and g(x), find (f/g)(x)

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Solve this system of three variables:

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Find the product of each: DOES NOT EXIST 2X3 2X2

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Evaluate the determinant of this 3×3 matrix: 1-2 3 0 -7 1 DOWNHILL – UPHILL (0+56+12)- (0+4-18) 68 – (-14) 82 (18+280+0)- (0+0-8) 3-4 1 3 -10 0 246+8 254

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Evaluate each function given: 1. f(a 2 ) 2. f(3b 4 )

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Graph each function: 1. f(x) = 3x – 4 2. f(x) = – ⅔ x + 1

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Find the values of x and y for which the matrix equation is true. I would use substitution:

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Given the two matrices, perform the following operations. A = B = 1. 3B 2. 2A – C Impossible

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Find the inverse of each matrix. 1. 2. Does not exist

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Graph each inequality: 1. 2x + y – 3 < 02. x + 3y – 6 ≥ 0

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Determine the intervals of increasing and decreasing for each function: Decreasing x < 1 Increasing x > 1 Decreasing -1.5 < x < 0.2 Increasing x 0.2

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What lines are symmetric to each function given: 1. 2. x = 0 y = 0 x = 4 y = -2

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Graph each function and it’s inverse. 1. 2. f(x) f -1 (x) f(x) f -1 (x)

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Determine whether the critical pt given is a max, min, or pt of inflection. 1. x = 0 2. x = 1 MAX MIN

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Approximate the real zero. 1. 2. x y -5 -65 -4 -25 -3 -5 -2 1 0 -5 1 -5 2 5 3 31 x y -5 435 -4 138 -3 19 -2 -6 -1 3 0 10 1 3 2 -6 3 19 So there is zeroes between – 3 and -2, – 2 and -1, 1 and 2 Rule of thumb: go from -5 to 5 for your x-values If they want a decimal approximation, you need to make another t-chart going by 0.1 in between these approximated zeros. Or you could just plug each answer and see which one gets you closest to a ZERO

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Solve the system of inequalities by graphing

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Use the related function to find the min and max. 1. 2.

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Determine the vertical asymptotes of each function VA: x = 0 VA: x = ⅓ VA: x = 4, x = 0

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Graph each rational function Hole at x = -2 Hole at x = 0

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Find the roots of: A.) B.) C.) 2, -1 D.) -2, 1 USE THE COMMON ROOT AND DO SYNTHETIC DIVISION FIRST 2 IS COMMON AMONG ALL THE ANSWERS AFTER SYNTHETIC DIVISION, TRY TO FACTOR, OR QUADRATIC FORMULA TO FIND THE REST OF THE ROOTS.

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Find the number of positive, negative, and imaginary roots possible for this function: 3, 1 positive roots 0 Negative roots P N I 3 0 2 1 0 4 Each row adds up to degree of polynomial In a polynomial equation, if there is four changes in signs of the coefficients of the terms, __________________________ there is 3 or 1 positive roots

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Using Law of Sines 1.In ΔABC if A = 63.17°, b = 18, and a = 17, find B 2. In ΔABC if A = 29.17°, B = 62.3°, and c = 11.5, find a

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Determine the type of discontinuity for each function:

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Find the maximum value for this system of inequatilites: Infeasible? Unbounded? Optimal solutions?

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Solve this rational inequality: Use a number line

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Find this trig value: 1. Given

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Evaluate each problems using the unit circle:

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Determine for each function if it is odd, even, or neither? Odd functions are symmetric with respect to the origin: (a,b) and (-a,-b) Even functions are symmetric with respect to the y-axis: (a,b) and (-a,b) EVEN BOTH ORIGIN EVEN

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List all possible rational roots of each function: P: 1, 2, 5, 10 Q: 1 P: 1,3 Q: 1, 2, 4

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Use the triangles below to find missing cos A, sin A, tan A A 8 ft. 5 ft.

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Use the unit circle to find each: 0 undefined

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State the amplitude for each function: Amplitude = noneAmplitude = 2 Amplitude = 1

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Find the period for each function: Period = π/k = πPeriod = 2π/k = 2π/3 or 120° Period = 2π/k = 6π or 1080°

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Graph each function VA: x = -3 HA: y = 0 VA: x = 5 HA: y = 0

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