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# Final Exam Cards

### These will be supplimental for a final exam

What are Monomials? How do you solve them? Monomials: Are algebraic expressions that have only 1 term. -Multiply Numerators, and simplify. -Multiply Denominators and simplify. -Divide the Coefficients. -Subtract like bases (From numerator and denominator) To simply and get final answer.
What are Binomials? How do you solve them? Binomials: Bi = 2. These will have two terms. - Simplify! -Find the multiples of both numbers. -Set one to Positive, and the other to negative. -2x-49 (x-7)(x+7) = The "Zeros"
What are Trinomials? How do you solve them? Trinomials: Expressions with three terms. - Look at the middle term. What TWO numbers will add to get that, and multiply to get the LAST term? -Simply figure this out, and you will get your zeros.
Who is BeN? Why does he help in exponential equations? Ben is Base - The base of the logarithm. Exponent - The small number above. Number - The Number or output. - This tells us how an exponential equation is composed. BASE,EXPONENT, then NUMBER.
Who is BNE, or Bennie? How does it help with logarithmic equations? BNE = Base Number Exponent -To convert an exponential equation into a logarithmic equation. -Replace BEN with BNE.
What do you need to include when graphing polynomial finctions? 1.) Zeros 2.) Test points 3.) The End behavior 4.) Graph (Of course.)
How do you figure out the turning points of a polynomial? The degree. (Highest exponent.) Minus 1 will determine this.
What is a Turning point? An X value where a local maximum or minimum occurs.
How do you determine the End Behavior of a graph? -POSITIVE and EVEN. Both points go up. -POSITIVE and ODD. Right arm goes up, left arm goes down -NEGATIVE and EVEN. Both points go down. -NEGATIVE and ODD. left arm goes down right arm up
What is a Vertical Asymptotic? VERTICAL lines that occur from the DENOMINATOR of a rational.
How can you find ALL the zeros of a polynomial? 1.)Synthetic Division 2.)Long Division 3.)Factoring 4.)Graphing. - If having trouble on one, go to another.
What is a Function? -Passes vertical line test -Has only ONE input. One unique X value.
How do you know when there's a horizontal asymptote? This will only happen when there is a VERTICAL shift.
How do you solve a peace wise function? These are like puzzles! -You must look if the greater than or less than has a line under it. -Line = Closed circle. No line = Open Circle. -solve the peace wise in the way the problem asks you to. x>0 means that it will be ALL of the values over 0.
Quadratic formula. x=-b±sqrt/b^2-4ac 2a REMEMBER -B- No bees! ±2 4 - AIR CONDITIONING 2a 2 on top and 2a on bottom!
what is e? Where can You find it? "Natural Base" 2nd key, then division key. e = Approximately 2.718
What is the vertex formula? a(x-h)^2+k
When should I use Synthetic Division, as opposed to Long Divison? Synthetic division for smaller polynomials. 2x-4 is an example. Long division can do ALL other polynomials, but takes MUCH LONGER.
What are One to One Functions? Has EXACTLY 1 X value and 1 Y Value. -Passes Horizontal AND Vertical line test.
What is a negative exponent? Why do we NOT want this? A Negative exponent = the reciprocal of the number it's in front of. 1.) Simplify ALL Negative exponents to the reciprocal . 2.) Divide the fractions and simplify. 3.) Times ALL Denominators by each part. 4.) Simplify and solve.

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