The slope of a line is the ratio of vertical travel to horizontal travel, whether on a coordinate plane or in the real world. It can be positive or negative.
On an x-y plane, to find the slope of a line you would identify the coordiates of two points on the line, then form the ratio
slope = (difference of y-coordinates)/(difference of corresponding x-coordinates)
Given two points (x1, y1) and (x2, y2), the slope is computed as
slope = (y2 - y1)/(x2 - x1)
The points can be used in the computation in either order and the result will be the same. It is often convenient to have x2 > x1, so the denominator is positive. This can reduce errors in the arithmetic, but it is not required.
If the line is a vertical line, so that all x-values are the same, the slope is said to be "undefined."
On a conventionally drawn coordinate plane, a line with positive slope will go up to the right (/); a line with negative slope will go down to the right (\).
Answer:
- (f - g)(x) = x⁴ - x³ - 2x² - 4x + 12
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<h3>Given</h3>
Functions f an g
- f(x) = x⁴ − 4x² + 4
- g(x) = x³ − 2x² + 4x − 8
<h3>Find the composite function (f - g)(x)</h3>
- (f - g)(x) =
- f(x) - g(x) = x⁴ - 4x² + 4 - (x³ −-2x² + 4x - 8) =
- x⁴ - 4x² + 4 - x³ + 2x² - 4x + 8 =
- x⁴ - x³ - 2x² - 4x + 12