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Chapter 1 vocabulary

Chapter 1 vocabulary. Section 1.1 Vocabulary. Exponential, logarithmic, Trigonometric, and inverse trigonometric function are known as Transcendental functions.

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Chapter 1 vocabulary

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  1. Chapter 1 vocabulary

  2. Section 1.1 Vocabulary

  3. Exponential, logarithmic, Trigonometric, and inverse trigonometric function are known as Transcendental functions.

  4. A linear function is an equation for a straight lineand can be written in the form y = mx + bwhere m is the slope and b is the y-intercept

  5. The Slope(m) of a nonvertical line represents the number of units the line rises or falls vertically for each unit of horizontal change from left to right.

  6. y = mx + b is known as the slope intercept form of the equation of a line.

  7. The point-slope form of the equation of a line that passes through the point (x1 , y1) is y - y1 = m(x - x1)

  8. The general form for the equation of a line isAx + By + C = 0where A and B are not both zero

  9. Two distinct lines are parallel if and only if their slopes are the same.

  10. Two distinct lines are perpendicular if and only if their slopes are negative reciprocals of eachother.

  11. Section 1.2 Vocabulary

  12. Function- each member of the domain (x-values) is pairedwith EXACTLY one member of the range (y-values).

  13. Function Notation: y = f(x) fis the name of the function y is the dependent variable, or output value x is the independent value, or input value

  14. The Domain of a function is the set of all values( x- values/ inputs) of the independent variable for which the function is defined.

  15. The Range of a function is the set of all values ( y-values/ outputs) assumed by the dependent variable.

  16. The difference Quotient: f(x + h) - f(x) , h ≠ 0 h

  17. Section 1.3 vocabulary

  18. The graph of a function f is the collection of ordered pairs (x, f(x)) such that x is in the domain of f

  19. Vertical line testA set of points in a coordinate plane is the graph of y as a function of x iff no vertical line intersects the graph at more than one point.

  20. A function f is increasing on an interval if, for any x1 and x2 in the interval, x1 < x2 implies f(x1) < f(x2).

  21. A function f is Decreasing on an interval if, for any x1 and x2 in the interval, x1 < x2 implies f(x1) > f(x2).

  22. A function f is constant on an interval if, for any x1 and x2 in the interval, f(x1) = f(x2).

  23. A function value f(a) is called a relative minimum of f if there exists an interval (x1, x2) that contains a such that x1< x < x2 implies that f(a) ≤ f(x)

  24. A function value f(a) is called a relative maximum of f if there exists an interval (x1, x2) that contains a such that x1< x < x2 implies that f(a) ≥ f(x).

  25. A function whose graph is symmetric with respect to the y-axis is an even function.f(-x) = f(x)

  26. A function whose graph is symmetric with respect to the origin is an odd function.f(-x) = -f(x)

  27. Section1.4 Vocabulary

  28. Vertical and Horizontal Shifts Let c be a positive real number. Vertical and horizontal shifts in the graph y = f(x) are as follows: • 1. Vertical shift c units up h(x) = f(x) + c • 2. Vertical shift c units down h(x) = f(x) – c • 3. Horizontal shift c units right h(x) = f(x-c) • 4. Horizontal shift c units left h(x) = f(x+c)

  29. Reflections in the Coordinate axes Reflections in the coordinate axes of the graph y = f(x) are as follows: • Reflection in the x-axis h(x) = -f(x) • Reflection in the y-axis h(x) = f(-x)

  30. Horizontal shifts, vertical shifts, and reflections are called rigid transformations because the shape of the graph is unchanged.

  31. Nonrigid transformations change the shape of the graph.

  32. A nonrigid transformation of the graph y = f(x) is represented by y=cf(x), where the transformation is a vertical stretch if c > 1

  33. A nonrigid transformation of the graph y = f(x) is represented by y=cf(x), where the transformation is a vertical shrink if 0 < c < 1

  34. A nonrigid transformation of the graphy = f(x) is represented by h(x) = f(cx). If c > 0 it is a horizontal shrinkIf 0 < c < 1 then it is a horizontal stretch

  35. Section 1.5 Vocabulary

  36. Arithmetic Combinations • Sum: (f + g) (x) = f(x) + g(x) • Difference: (f – g) (x) = f(x) – g(x) • Product: (fg)(x) = f(x) g(x) • Quotient (f/g) (x) = f(x) / g(x)

  37. The composition of the function f with the function g is (f o g)(x) = f(g(x)) Note: The domain of (f o g) is the set of all x in the domain of g such that g(x) is in the domain of f

  38. Section 1.6 Vocabulary

  39. By switching the first and second coordinates of the ordered pairs of a function you can form the inverse function, which is denoted f-1(x).

  40. Definition of Inverse function • Let f and g ve two functions such that f(g(x)) = x, for all x in the domain of g And g(f(x)) = x for all x in the domain of f Thus, g(x) is an inverse function of f(x), and g(x) Can be denoted as f-1(x).

  41. To have an inverse a function must be one-to-one, which means that no two elements in the domain of f correspond to the same element in the range of f

  42. Finding a linear model to represent the relationship described by a scatter plot is called fitting a line to data.

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