# Graph of a Curve Continuity This curve is _____________These curves are _____________ Smoothness This curve is _____________These curves are _____________.

## Presentation on theme: "Graph of a Curve Continuity This curve is _____________These curves are _____________ Smoothness This curve is _____________These curves are _____________."— Presentation transcript:

Graph of a Curve Continuity This curve is _____________These curves are _____________ Smoothness This curve is _____________These curves are _____________ y x y x y x y x y x y x

Graph of a Curve (contd) Increasing A function f is increasing on an open interval I if, for any x 1 and x 2 in I, with x 1 < x 2, we have f(x 1 ) < f(x 2 ). Decreasing A function f is decreasing on an open interval I if, for any x 1 and x 2 in I, with x 1 f(x 2 ). Constant A function f is constant on an open interval I if, for any x 1 and x 2 in I, we have f(x 1 ) = f(x 2 ). x y x1x1 x2x2 I f(x1)f(x1) f(x2)f(x2) y x x1x1 x2x2 I f(x1)f(x1) f(x2)f(x2) y x x1x1 x2x2 I f(x1)f(x1)f(x2)f(x2) Local (or Relative) Extrema A function f has a local maximum at x = x 0 if locally, f(x 0 ) is greater than all the surrounding values of f(x). We call this f(x 0 ) a local maximum of f. A function f has a local minimum at x = x 0 if locally, f(x 0 ) is less than all the surrounding values of f(x). We call this f(x 0 ) a local minimum of f. x1x1 x2x2 x3x3 f(x 3 ) is a _____________ f(x 1 ) is a ___________________________ f(x 2 ) is a ______________ Global (or Absolute) Extrema A function f has a global maximum at x = x 0 if f(x 0 ) is greater than or equal to all values of f(x). We call this f(x 0 ) the global maximum of f. A function f has a global minimum at x = x 0 if f(x 0 ) is less than or equal to all values of f(x). We call this f(x 0 ) the global minimum of f.

Use each graph to find the domain and range of the function: -5-4-3-212345 -4 -3 -2 1 2 3 4 -5-4-3-212345 -4 -3 -2 1 2 3 4 Domain = _______________ Range = _______________ Domain = _______________ Range = _______________ -5-4-3-212345 -4 -3 -2 1 2 3 4 -5-4-3-212345 -4 -3 -2 1 2 3 4 Domain = _______________ Range = _______________ Domain = _______________ Range = _______________

1) Find f(5), f(2), and f(–6): f(5) = ___, f(2) = ___, f(–6) = ___ Use the graph of the function f given below to answer the following questions: 2) Is f(–1) positive? ___ f(5)? ___ 3) Is f(2) negative? ___ f(–4)? ___ 4) What is the domain of f ? ________ 5) What is the range of f ? _________ 6) What are the x-intercepts? _______ 7) What is the y-intercept? ___ 11) How often does the line y = 1 intersect the graph? ___ y = ½? ___ y = –2? ___ 10) For what value(s) of x does f(x) = 0? _______ f(x) = 1? _____ 8) Is f continuous? _______ 9) Is f smooth? _______ 12) List the interval(s) on which f is decreasing? ______________ 13) List the interval(s) on which f is increasing? ______________ 14) List the interval(s) on which f constant? _______________ 15) If any, list all the local maxima? ______ At which x values? ______ 16) If any, list all the local minima? ______ At which x values? ______ 17) Is there any global maximum? _____ global minimum? _____ -9-8-7-6-5-4-3-2123456 -4 -3 -2 1 2 3 4

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