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In addition to interpreting functions in context, it can be worthwhile to analyze the graphs of functions in terms of key features, which include the following.
The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. The y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis. The y-intercept of an equation is also known as its initial value.
When talking about functions, the x-intercepts are the zeros of the function. Sometimes, only one coordinate of these points is referenced. For example, if the x-intercept lies at (a,0), it can be said that the x-intercept is at x=a. The same is true for the y-intercept. A relation can have several intercepts. A function can have multiple x-intercepts, but it can only have one y-intercept.The value f(c) is a relative minimum, or local minimum, of a function if f(c) is the least output of f around x=c. Likewise, the value f(d) is a relative maximum, or local maximum, of a function if f(d) is the greatest output of f around x=d.
If the function is continuous, the function switches from increasing to decreasing at a relative maximum or from decreasing to increasing at a relative minimum.There are two types of symmetry that the graph of a function can have — even or odd. A function has even symmetry if it is symmetric with respect to the y-axis. In other words, if the y-axis cuts the graph into two mirror images.
Notice that if the graph were folded vertically on the y-axis, the marked points would lie on top of each other. This is true for every point on f. Thus, f(x) has even symmetry. A function is said to have odd symmetry if it's symmetric about the origin. In other words, if one half of the graph can be rotated 180∘ to match the other half of the graph exactly.
Notice that the portion of the graph below the y-axis could be rotated so that it lies directly on top of the portion above the y-axis. Thus, f has odd symmetry.up.
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