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Chapter 3 Review Pre-Calculus

Chapter 3 Review Pre-Calculus. Determine what each graph is symmetric with respect to. y-axis, x-axis, and origin. y-axis, x-axis, origin, y = x, and y = -x. y-axis. The graph of each equation is symmetric with respect to what?.

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Chapter 3 Review Pre-Calculus

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  1. Chapter 3 ReviewPre-Calculus

  2. Determine what each graph is symmetric with respect to y-axis, x-axis, and origin y-axis, x-axis, origin, y = x, and y = -x y-axis

  3. The graph of each equation is symmetric with respect to what? Two squared terms, with same coefficients means it is an circle with center (0, 0) Two squared terms, but different coefficients means it is an ellipse with center (0, 0) One squared term means it is a parabola shifted up 5 units and more narrow. Symmetric with respect to x-axis, y-axis, origin, y = x, and y = -x Symmetric with respect to the y-axis Symmetric with respect to x-axis, y-axis, and origin

  4. Graph each equation:

  5. Graph each equation:

  6. Determine whether each function is even, odd or neither. Figure out f(-x) and –f(x) If all the signs are opposite, then the function is EVEN

  7. Determine whether each function is even, odd or neither. Figure out f(-x) and –f(x) If all the signs are opposite and the same, then the function is NEITHER even or odd.

  8. Determine whether each function is even, odd or neither. Figure out f(-x) and –f(x) If all the signs are the same, then it is ODD

  9. Describe the transformation that relates the graph of to the parent graph THREE UNITS TO THE LEFT Describe the transformation that relates the graph of to the parent graph THREE UNITS UP, AND MORE NARROW Describe the transformation that relates the graph of to the parent graph FOUR UNITS TO THE RIGHT, AND THREE UNITS UP

  10. Describe the transformations that has taken place in each family graph. Right 5 units Up 3 units More Narrow More Narrow, and left 2 units

  11. Describe the transformations that has taken place in each family graph. More Wide, and right 4 units Right 3 units, and up 10 units More Narrow Reflected over x-axis, and moved right 5 units

  12. Describe the transformations that has taken place in each family graph. Reflect over x-axis, and up 2 units Reflected over y-axis Right 2 units

  13. FINDING INVERSE FUNCTIONS Find the inverse of ,

  14. FINDING INVERSE FUNCTIONS Find the inverse of f (x) = 4x + 5

  15. Find the inverse of f (x) = 2x3 - 1

  16. Find the inverse of

  17. Find the inverse of Steps for finding an inverse. • solve for x • exchange x’s • and y’s • replace y • with f-1

  18. Graph then function and it’s inverse of the same graph. Parabola shifted 4 units left, and 1 unit down Now to graph the inverse, just take each point and switch the x and y value and graph the new points. Ex: (-4, -1) becomes (-1, -4) Finally CHECK yourself by sketching the line y = x and make sure your graphs are symmetric with that line.

  19. Graph then function and it’s inverse of the same graph. Cubic graph shifted 5 units to the left Now to graph the inverse, just take each point and switch the x and y value and graph the new points. Ex: (-5, 0) becomes (0, -5) Finally CHECK yourself by sketching the line y = x and make sure your graphs are symmetric with that line.

  20. Graph then function and it’s inverse of the same graph. Parabola shifted down 2 units Now to graph the inverse, just take each point and switch the x and y value and graph the new points. Ex: (0, -2) becomes (-2, 0) Finally CHECK yourself by sketching the line y = x and make sure your graphs are symmetric with that line.

  21. Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

  22. Determine if each parabola has a maximum value or a minimum value. y = ax2 + bx + c “a” is positive so that means it opens up, and has a minimum “a” is negative so that means it opens down, and has a maximum

  23. Graph each inequality:

  24. Find the maximum point of the graph of each:

  25. Find the x and y intercepts of

  26. Without graphing, describe the end behavior of the graph of Positive coefficient, even power means it rises right and left Negative coefficient, even power means it falls right and left positive coefficient, odd power means it rises right and falls left

  27. Without graphing, describe the end behavior of the graph of Positive coefficient, even power means it rises to left and falls to right Positive coefficient, odd power means it rises right and falls left positive coefficient, even power means it rises right and rises left

  28. Part Two

  29. Determine whether each function is even, odd, or neither.

  30. Graph the function Find the inverse equationGraph the inverse on the same graph. Is the inverse a function?

  31. Determine the asymptotes for the rational function then graph it

  32. Graph the inequality

  33. Find the derivative of the function

  34. Find the derivative of the function

  35. Find the equation of the tangent to y = x3 + 2x at: A.) x = 2 B.) x = -1 C.) x = -2

  36. Question: If the tangent line to a point of f(x) was horizontal, what would that tell us about f’(x)? f’(x)=0

  37. Example: Find the coordinates of any points on the curve with the equation f(x)= x3 + 3x2 - 9x + 5 where the tangent is horizontal. Step 1: Find the derivative, f’(x) Step 2: Set derivative equal to zero and solve, f’(x)=0 Step 3: Plug solutions into original formula to find y-value, (solution, y-value) is the coordinates. Note: If it asks for the equation then you will write y=y value found when you plugged in the solutions for f’(x)=0

  38. Example: Find the coordinates of any horizontal tangents to y = x3 - 12x + 2

  39. Determine three critical points that are found on the graph of .Identify each equation as a relative max, min, or point of inflection.

  40. Find the x and y intercept of

  41. Sketch the graph ofDescribe the graph.

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