Properties of a function from its graph
From the graph of a function on [−4; 7], find its zeros, the intervals where it keeps one sign, an interval of increase and its greatest value. This follows the Ukrainian Year 9 algebra book, section 8 "Properties of a function".
- سوريا: الصف ١٠
- فلسطين: الصف ٩
- أوكرانيا: الصف ٩
- روسيا: الصف ٧
- ألمانيا: الصف ٨
- فرنسا: الصف ١٠
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الدليل
In the Ukrainian Year 9 algebra book (section 8, "Properties of a function") the properties of y = f(x) are read from its graph. The picture shows a function defined on the interval [−٤، ٧]: this is its domain, D(f) = [ − ٤;٧]. The greatest value is 4 and the least is −3, so its range is the interval [−٣، ٤].
A zero of a function is a value of the argument for which the value of the function is zero. Here they are −3, 1 and 5: the graph crosses the x-axis there.
An interval of constant sign is an interval on which the function takes values of the same sign. The zeros are never inside such an interval, so they are left out with round brackets. Always give the intervals as long as possible.
A function is increasing on an interval if for any two values x١ and x٢ of the argument in it with x٢ > x١ we have f(x٢) > f(x١). It is decreasing if f(x٢) < f(x١). On the graph, walk along the x-axis from left to right: it increases where the graph goes up. The greatest and least values are values of y, not of x.