Function properties – examples
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1) What will you learn in the video? What does the video follow up on? What do we already know? link to the video with the theory Properties of functions: • Properties of functions 2) Determining the properties of a function that is given by its graph – 14 examples domain of definition domain of values increasing, decreasing, non-increasing, non-decreasing, constant increasing, decreasing, constant on an interval/set bounded, bounded from below, bounded from above global maxima and minima (at the point + value) simplicity periodicity evenness, oddness coordinates of the intersections of the graph of the function with the coordinate axes x, y continuity (from example 4) 3) Expanding on example 4: what is a signum function what is continuity of a function (only from the graph, without definition) 4) For example 3: Why do we distinguish, for example, increasing on (1; 2), increasing on (3; 5) and increasing on (1; 2) ∪ (3; 5)? 5) For example 12: Why is it more important for us to determine at which point the extrema of the function are located than the function value at these points? 6) Extension of example 14: what is a local maximum (difference from the global maximum) what is concavity, convexity and inflection point 7) Example: Determine the coordinates of the intersections of the graph of a function with the coordinate axes x, y, if the function given by the formula f: y = 4x - 2 g: y = (3x + 8) / (3x - 2) 8) Example: Determine whether the function given by the formula is even, odd or neither f: y = x^2 - 2x + 7 ... neither g: y = (x^4)/2 - 7x^2 + 1 ... even h: y = 3 / (x - 1) + 4 ... neither h2: y = 3/(x^2) - (x + 1) / (x + 1) ... neither f2: y = (4x^3 - 5x) / (2x) ... even f3: y = (4x^3 - 5x) / 2 ... odd y = 0 ... even and odd 9) Example: Determine the domain of the function given by the formula f: y = (5x^21 - (π^3)*x + 64 - √5) / (x^2 - x - 12) + 1/√(x + 5) - √(10 + x) 10) Summary
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