Algebra 2 Tri-B Review!. LogarithmsSolving Polynomials Compostion of Functions & Inverses Rational Expressions Miscellaneous 200 400 600 800 1000.

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Presentation transcript:

Algebra 2 Tri-B Review!

LogarithmsSolving Polynomials Compostion of Functions & Inverses Rational Expressions Miscellaneous

Logarithms 200 Write in exponential form: Write in exponential form: log 32 8=3/5 log 32 8=3/5 Write in log form: Write in log form: 9 0 =1 9 0 =1 Answer

Logarithms 200 Answer log 32 8=3/5  8 3/5 =32 log 32 8=3/5  8 3/5 = =1  log 9 1=0 9 0 =1  log 9 1=0 Question Board

Logarithms 400 Condense: Condense: log log 2 x+6log 2 y log log 2 x+6log 2 y Expand: Expand: Answer

Logarithms 400 Answer Condense: Condense: log log 2 x+6log 2 y = log 2 5x 2 y 6 log log 2 x+6log 2 y = log 2 5x 2 y 6 Expand: Expand: = 5logx+3logy-4logz Question Board

Logarithms 600 Solve: Solve: Answer

Logarithms 600 Answer 2 3x = x = x=-6 3x=-6 x = -2 x = -2 Question Board

Logarithms 800 log 2 (8-5b) = log 2 (b+2) log 2 (8-5b) = log 2 (b+2) log4 + logx = log64 log4 + logx = log64 Answer

Logarithms 800 Answer log 2 (8-5b) = log 2 (b+2) log 2 (8-5b) = log 2 (b+2) 8-5b = b+2 6=6bb=1 log4 + logx = log64 log4 + logx = log64 log4x = log64 4x=64x=16 Question Board

Logarithms log 8 (9x-3) = log 8 (9x-3) = -13 Answer

Logarithms 1000 Answer log 8 (9x-3) = log 8 (9x-3) = -13 x = 25/72 x = 25/72 Question Board

Solving Polynomials 200 Write an equation for a polynomial with zeros 4, -1, and 9. Write an equation for a polynomial with zeros 4, -1, and 9. Make sure to foil completely! Answer

Solving Polynomials 200 Answer f(x) = (x-4)(x+1)(x-9) f(x) = (x-4)(x+1)(x-9) f(x) = x 3 -12x 2 +23x+36 f(x) = x 3 -12x 2 +23x+36 Question Board

Solving Polynomials 400 Find all the zeros using the graphing calculator: Find all the zeros using the graphing calculator: f(x) = 2x 3 + 9x 2 – 8x - 15 f(x) = 2x 3 + 9x 2 – 8x - 15 Answer

Solving Polynomials 400 Answer x = -5, 3/2, 5 x = -5, 3/2, 5 Question Board

Solving Polynomials 600 Answer Find the remaining zeros. Find the remaining zeros.

Solving Polynomials 600 Answer a = 1, b = 0, c = 4 a = 1, b = 0, c = 4 x = 2i, -2i, 3 Question Board

Solving Polynomials 800 Find the remaining zeros: Find the remaining zeros: f(x) = x 3 – 16x x – 114; x=6 f(x) = x 3 – 16x x – 114; x=6 Answer

Solving Polynomials 800 Answer Question Board

Solving Polynomials 1000 Find all the zeros: Find all the zeros: x =0 x =0 Answer

Solving Polynomials 1000 Answer Question Board

Composition & Inverses of Functions 200 f(x) = 3x+2 f(x) = 3x+2 g(x) = x 2 +3x g(x) = x 2 +3x Find f(g(2)) and g(f(2)). Find f(g(2)) and g(f(2)). Answer

Composition & Inverses of Functions 200 Answer f(g(2)) = -4 f(g(2)) = -4 g(f(2)) = 88 g(f(2)) = 88 Question Board

Composition & Inverses of Functions 400 Find the inverse of: Find the inverse of: Answer

Composition & Inverses of Functions 400 Answer Question Board

Composition & Inverses of Functions 600 h(x) = x 2 -x h(x) = x 2 -x g(x) = 3x+4 g(x) = 3x+4 Find h(g(x)). Find h(g(x)). Answer

Composition & Inverses of Functions 600 Answer h(x) = x 2 -x h(x) = x 2 -x g(x) = 3x+4 g(x) = 3x+4 h(g(x)) = 9x 2 +21x+12 h(g(x)) = 9x 2 +21x+12 Question Board

Composition & Inverses of Functions 800 Find the inverse of f(x), then find f -1 (f -1 (x)) Find the inverse of f(x), then find f -1 (f -1 (x)) (or “the composition of the inverse with itself”) Answer

Composition & Inverses of Functions 800 Answer f -1 (x) = 2x+8 f -1 (x) = 2x+8 f -1 (f -1 (x)) = 4x+24 f -1 (f -1 (x)) = 4x+24 Question Board

Composition & Inverses of Functions 1000 g(a) = a 2 – 1 g(a) = a 2 – 1 h(a) = 3a h(a) = 3a Find g(h(a)) then find the inverse of that new function. Find g(h(a)) then find the inverse of that new function. (remember to simplify when possible!) Answer

Composition & Inverses of Functions 1000 Answer g(h(a)) = 9a 2 – 1 g(h(a)) = 9a 2 – 1 Inverse of 9a 2 – 1: Inverse of 9a 2 – 1: Question Board

Rational Expressions 200 Simplify the following: Simplify the following: Answer

Rational Expressions 200 Answer Question Board

Rational Expressions 400 Simplify the following: Simplify the following: Answer

Rational Expressions 400 Answer Question Board

Rational Expressions 600 Simplify the following: Simplify the following: Answer

Rational Expressions 600 Answer Question Board

Rational Expressions 800 Simplify the following: Simplify the following: Answer

Rational Expressions 800 Answer Question Board

Rational Expressions 1000 Simplify the following: Simplify the following: Answer

Rational Expressions 1000 Answer Question Board

Miscellaneous x = 43 2 x = 43 Round to 2 decimal places. Round to 2 decimal places. Answer

Miscellaneous 200 Answer x = 5.43 x = 5.43 Question Board

Miscellaneous 400 Find the remaining zeros: Find the remaining zeros: f(x) = 3x 5 – 25x 4 +56x 3 + 8x 2 – 59x + 17 f(x) = 3x 5 – 25x 4 +56x 3 + 8x 2 – 59x + 17 x=4+i x=4+i Answer

Miscellaneous 400 Answer x = 1/3, -1, 1, 4+i, 4-i x = 1/3, -1, 1, 4+i, 4-i Question Board

Miscellaneous x-3 = 4 7 2x-3 = 4 Round to 2 decimal places. Round to 2 decimal places. Answer

Miscellaneous 600 Answer 7 2x-3 = 4 7 2x-3 = 4 x = 1.86 x = 1.86 Question Board

Miscellaneous 800 Simplify the following: Simplify the following: Answer

Miscellaneous 800 Answer Question Board

Miscellaneous 1000 Simplify the following: Simplify the following: Answer

Miscellaneous 1000 Answer Question Board