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Understanding Precalculus

Understanding Precalculus. 1. Describe the patterns that govern the transformations of functions. What does the discriminate tell us about the roots of a quadratic.

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Understanding Precalculus

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  1. Understanding Precalculus 1. Describe the patterns that govern the transformations of functions. What does the discriminate tell us about the roots of a quadratic. In the quadratic formula, , is called the discriminate. When solving for the roots of a quadratic, we could have 3 different situations. The discriminate could be greater than zero. This would tell us that this quadratic would have two real roots. The discriminate could be equal to zero and this would tell us there is only one real root. If the discriminate was less than zero this would tell us that the quadratic has no real roots. It’s roots would be imaginary.

  2. Understanding Precalculus WHY would a graph NOT be continuous? Some functions have a limit in their domain example: many rational functions or functions involving even powered radicals. These limits, which if NOT addressed would result in the function being undefined, create a “break” in the graph. In rational functions, this “break” results in a “hole” or in a asymptote. How does the Leading Coefficient test help us graph? The leading coefficient test helps us graph because it pinpoints where a zero or x intercept is located. By substituting values for x into a function as it approaches the x axis we can determine when the function crosses the x axis because the sign on y value associated with the x value we use will change from either a negative value to a positive value or visa versa.

  3. Understanding Precalculus 5. How do we find the zeros of a polynomial function? We have many “tools” that aid us in finding the zeros of a polynomial. These tools all require us to find f(x) = 0. By substituting zero in for y and then solving the polynomial we can determine these zeros. On linear functions we could simply solve, on quadratics we could use factoring, quadratic formula or solving using square roots, on higher power polynomials we could use factoring by grouping, solving, the Intermediate Value thm, (which involves trial and error test points) or the Rational Root thm (which requires p/q and then factoring and quadratic formula.) 6. All continuous graphs are NOT functions. A vertical line is a continuous graph and it is not a function. So is the graph of a circle or an ellipse. 7. Give an example of a power function that is odd.

  4. 8. Explain “end behavior”. End behavior describes the behavior of a graph as the x approaches negative and positive infinity. For example , in a cubic as x approaches negative infinity f(x) approaches positive infinity on the left while on the right, as x approaches positive infinity f(x) approaches positive infinity. End behavior helps us determine the shape of a graph at its ends. 9. Sketch a graph that has at least one multiple root.

  5. 10. How can the Intermediate value thm help up graph? See my answer from number 5. Give an example of a polynomial written in : Standard form: + b. Not Standard form: + How many turning points does this function have? 5. 13. Why could a roller coaster be a great example of turning points?

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