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What function family does the function f(x)=2x-17 represent?

User Liezel
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Final answer:

f(x)=2x-17 represents a linear function, which is characterized by a constant rate of change and a straight-line graph, unlike even and odd functions which exhibit symmetry along axes.

Step-by-step explanation:

The function f(x)=2x-17 represents a linear function, which is part of the family of linear functions. A linear function has the general form f(x)=mx+b where m represents the slope and b represents the y-intercept. In the case of the function f(x)=2x-17, the slope m is 2 and the y-intercept b is -17.

When we think about the graphical representation of this function, we understand that it will be a straight line with a slope of 2, crossing the y-axis at (0, -17). This type of function displays a constant rate of change, which is evident in its graph as a straight line. In contrast, even and odd functions, like y(x) = −y(-x), showcase a different type of symmetry along the axes, which is not a characteristic of linear functions. Similarly, the function f(x) being restricted between x=0 and x=20 makes no difference to its classification as a linear function.

When considering other function types, such as exponential or quadratic functions, we see a different behavior. For example, if at x=3 a function has a positive value with a positive, decreasing slope as x increases, it may indicate a quadratic function like y=x², because linear functions like y=13x do not have a changing slope.

User Chtioui Malek
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