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Section 4.1
- Dr. Doug Ensley
Section 4.1 Dr. Doug Ensley February 9, 2015 Linear Functions A - - PowerPoint PPT Presentation
Section 4.1 Dr. Doug Ensley February 9, 2015 Linear Functions A - - PowerPoint PPT Presentation
Section 4.1 Dr. Doug Ensley February 9, 2015 Linear Functions A linear functions defining property is that the slope between any two points is the same. Linear Functions A linear functions defining property is that the slope between any
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Linear Functions
A linear function’s defining property is that the slope between any two points is the same. Example 1 Is this data from a function that’s linear or nonlinear? If linear, what is the slope? x 1 2 5 6 8 y = f (x) 20 17 8 5
- 1
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Linear Functions
A linear function’s defining property is that the slope between any two points is the same. Example 1 Is this data from a function that’s linear or nonlinear? If linear, what is the slope? x 1 2 5 6 8 y = f (x) 20 17 8 5
- 1
In this example, no matter what two points you use, the slope between them is −3. Therefore, these points are consistent with a linear function with slope −3.
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Linear Functions
A linear function’s defining property is that the slope between any two points is the same.
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Linear Functions
A linear function’s defining property is that the slope between any two points is the same. Example 2 Is this data from a function that’s linear or nonlinear? If linear, what is the slope? x 1 3 4 6 y = g(x) 20 17 8 5 1
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Linear Functions
A linear function’s defining property is that the slope between any two points is the same. Example 2 Is this data from a function that’s linear or nonlinear? If linear, what is the slope? x 1 3 4 6 y = g(x) 20 17 8 5 1 This function is non-linear. For example. the slope between points (0, 20) and (1, 17) is −3, but the slope between (1, 17) and (4, 5) is −4.
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Linear Functions
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Linear Functions
(a) Slope is 1 4 and y-intercept is the point (0, −3)
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Linear Functions
(a) Slope is 1 4 and y-intercept is the point (0, −3) (c) Average rate of change is the same as slope, so 1 4
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Linear Functions
(a) Slope is 1 4 and y-intercept is the point (0, −3) (c) Average rate of change is the same as slope, so 1 4 (d) Slope is positive so this function is always increasing.
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Linear Functions
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Linear Functions
(a) f (x) = 0 when x = 3
- 2. This means the x-intercept of f is at
the point 3
2, 0
- .
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Linear Functions
(a) f (x) = 0 when x = 3
- 2. This means the x-intercept of f is at
the point 3
2, 0
- .
(b) f (x) > 0 when x > 3
- 2. That is, f (x) > 0 for all x in the
interval 3
2, ∞
- .
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Linear Functions
(a) f (x) = 0 when x = 3
- 2. This means the x-intercept of f is at
the point 3
2, 0
- .
(b) f (x) > 0 when x > 3
- 2. That is, f (x) > 0 for all x in the
interval 3
2, ∞
- .
(c) f (x) = g(x) is the same thing as 6x − 9 = −8x + 5, which happens when x = 1. This means that the two functions have the same y-value when x = 1.
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Linear Functions
(a) f (x) = 0 when x = 3
- 2. This means the x-intercept of f is at
the point 3
2, 0
- .
(b) f (x) > 0 when x > 3
- 2. That is, f (x) > 0 for all x in the
interval 3
2, ∞
- .
(c) f (x) = g(x) is the same thing as 6x − 9 = −8x + 5, which happens when x = 1. This means that the two functions have the same y-value when x = 1. (d) f (x) ≤ g(x) when x ≤ 1. That is, f (x) ≤ g(x) for all x in the interval (−∞, 1).
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Intersection of Two Lines
(e) We use part (c) and the fact that f (1) = g(1) = −3 to determine that the intersection point is (1, −3).
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Linear Functions
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