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Key features of linear functions
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On the xy-plane, a straight line can be drawn in 4 ways. They can be in any direction and pass through any two points.
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This means that straight lines can be:
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nnndecreasingn n nhorizontalnnn n n n nnn n n n nnn
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- An increasing graph means that as x values increase, the y values increase.n
- A decreasing graph means that as x values increase, the y values decrease.n
- A horizontal graph means that as x values change the y values remain the samen
- In a vertical graph the x value is constant. n
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Regardless of all different shapes, all linear functions have some common characteristics.
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Intercepts
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The word intercept, in mathematics, refers to a point where a line, curve or function crosses or intersects with the axes.
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- We can have x-intercepts: where the line, curve or function crosses the x-axis.n
- We can have y-intercepts: where the line, curve or function crosses the y-axis.n
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Linear functions might have:
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- an x-intercept only (in the case of a vertical line)n
- a y-intercept only (in the case of horizontal lines) n
- or most have 2 intercepts, both an x-and a y-intercept (in the case of increasing or decreasing functions)n
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End behavior
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The end or extrema behavior of a function is a description of what happens past the viewing zone, what happens with the function outside of the area we can see.
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Take this graph for example,
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We can see in this graph x values between -5 and 5, and y values between -1 and 6. But we know that the graph goes on and on in the same linear fashion.
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This is the end or extrema behavior. All linear functions share the same end behavior, with a linear function this extrema behavior is that the line continues forever in the same direction. No kinks, turns, or unexpected movement just continues in that direction forever.
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Practice questions
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Question 1
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Question 2
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Question 3
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Source: https://t-tees.com
Category: WHAT
