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Let’s Review Functions

Let’s Review Functions. Daily Questions……. How do I name polynomials? What is interval notation? 3 . What is the domain & range of a function? 4 . How do I find the intercepts of a functions graphically and algebraically?. Naming Polynomials. MONOMIALS: A. A monomial is _______________

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Let’s Review Functions

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  1. Let’s Review Functions Daily Questions……. How do I name polynomials? What is interval notation? 3. What is the domain & range of a function? 4. How do I find the intercepts of a functions graphically and algebraically?

  2. Naming Polynomials • MONOMIALS: • A. A monomial is _______________ • B. Some examples of monomials are: a number, variable, or a product of numbers and variables. x -20 4y -3a5

  3. POLYNOMIALS: A. A polynomial is the ________ or ___________ of monomials. monomial the sum B. An example of a polynomial in one variable, x, would be x3+6x2+12x+8 C. How many MONOMIALS are there in the above polynomial? 4

  4. The _________exponent in the polynomial determines the DEGREE OF A POLYNOMIAL in one variable. largest A. Example: The degree of –7x + 9 – 4x2 is ____ because ___ is the largest exponent in the polynomial. 2 2 B. Example: Find the degree of the following polynomial: x4 + 6x3 + 7x5 + 12x 5

  5. IV. STANDARD FORM A. The terms of a polynomial are in STANDARD FORM if they are ordered from left to right in ______________ order; which means from the ____________ exponent to the smallest. decreasing largest B. To write a polynomial in Standard Form, ______________ the terms of the polynomial in ______________ order according to the ________________ of the variables. arrange decreasing exponent

  6. IV. STANDARD FORM C. Example: Write 9 + x – 4x3 in standard form. – 4x3 + x + 9 D. Example: Write 3x2 – 2 + 4x – 5x3 in standard form. – 5x3 + 3x2 + 4x - 2

  7. V. Some polynomials have SPECIAL NAMES that are determined by the following: A. Their _________ or B. Their _________ of terms C. Look at the chart for an explanation. degree number

  8. Monomial 0 Constant • 1 Monomial 1 Linear • Binomial 2 Quadratic • 2 Binomial 3 Cubic • 3 Trinomial 2 Quadratic

  9. How do we write in interval notation? • x < 2…. • when you want include use a bracket [ • when you want to exclude use a parenthesis ( Let’s draw a number line first….

  10. Let’s do another type…. Draw a number line first….

  11. Domain and Range • Remember that domain is all the x-values (the input). • Remember that range is all the y-values (the output).

  12. (2,4) (4,0) (-1,-5) What is the domain of f(x)? Ex. 1 y = f(x) Domain

  13. What is the range of f(x)? (2,4) (4,0) (-1,-5) y = f(x) Range

  14. Determine the domain and range….

  15. With polynomials…. • The DOMAIN is always All Reals, • The RANGE will be: • All Reals, • Lower Boundary to infinity, • Negative infinity to Upper Boundary,

  16. What’s a zero? Zeros/x-intercepts/Solutions/Roots Where the graph crosses the x-axis

  17. Analyze the Graph of a Function x-intercepts Where the graph crosses the x-axis. Also called zeros.

  18. Zeros? X= -3, -1, 2

  19. y-intercepts Where the graph crosses the y-axis

  20. X and Y-intercepts Using Algebra To find the x-intercepts, substitute y = 0 into the equation. To find the y-intercepts, substitute x = 0 into the equation. Ex. 1 y = 2x + 4 Ex. 2 y = x2 - 9

  21. Analyze the Graph of a Function y-intercepts

  22. Find the following • Domain: • Range: • 3. Zeros: • 4. y-intercepts: All reals All reals -2, 1 (0, -4)

  23. Find the following • Domain: • Range: • 3. Zeros: • 4. y-intercepts: All reals [-4, ∞) -2, 2 (0, -4)

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