Answer:
The graph of the function f(x) = (x - 3)(x + 1)
1 answer:
Answer:
The graph is positive and decreasing for all real values of x where x < -1
Step-by-step explanation:
we have
The function is a vertical parabola open up
The roots (x-intercepts) are x=3 and x=-1
The vertex is the point (1,-4 ) is a minimum
using a graphing tool
see the attached figure
we know that
In the interval (-∞,-1) ---> the function is positive and decreasing
In the interval (-1,1) ---> the function is negative and decreasing
In the interval (1,3) ---> the function is negative and increasing
In the interval (3,∞) ---> the function is positive and increasing
therefore
The graph is positive and decreasing for all real values of x where x < -1
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By applying the concept of <em>rigid</em> transformation and the equation of translation we conclude that the coordinates of points K' and M' are (-2, 3) and (-4, 1).
<h3>How to apply a translation to a point on a Cartesian plane</h3>
<em>Rigid</em> transformations are transformations applied onto <em>geometric</em> loci such that Euclidean distance is conserved at every point of the loci. Translations are an example of <em>rigid</em> transformations, whose formula is defined by the following expression:
(1)
Where:
- P(x, y) - Original point
- P'(x, y) - Resulting point
- Translation vector
If we know that K(x, y) = (4, 1), M(x, y) = (2, -1) and , then the coordinates of points K' and M' are:
Point K'
K'(x, y) = (4, 1) + (-6, 2)
K'(x, y) = (-2, 3)
Point M'
M'(x, y) = (2, -1) + (-6, 2)
M'(x, y) = (-4, 1)
By applying the concept of <em>rigid</em> transformation and the equation of translation we conclude that the coordinates of points K' and M' are (-2, 3) and (-4, 1).
To learn more on translations: brainly.com/question/17485121
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