Transformation of a function includes the changing of the location of the graph of the function on the coordinate plane. The formula of the function for transformation is slightly altered
(a) Please find attached the required graph of the functions g(x) and g(-x) + 2
(b) Please find attached the required graph of the functions y = f(x) and y = 2·f(x) - 3
a) Function transformations include move up or down, left or right,
The required transformation is g(x) to g(-x) + 2
The function that represent reflection of y = f(x) across the y-axis is the graph f(-x)
Similarly, the coordinates of the image of the point (x, y), following the reflection across the y-axis is the point (-x, y)
The coordinates of (x, y) following a displacement 2 units upwards is (x, y + 2)
The coordinates of the points of the graph are;
(-2, -4), (0, 0), and (4, -2)
Therefore, we get;
(-2, -4), (0, 0), and (4, -2)
(-2, -4) → g(x) to g(-x) + 2 → (2, -2)
(0, 0) → g(x) to g(-x) + 2 → (0, 2)
(4, -2) → g(x) to g(-x) + 2 → (-4, 0)
Therefore, with the points, (2, -2), (0, 2), and (-4, 0)
The graph of the function (created with MS Excel is plotted using the above coordinate point values and attached here
(b) The given points on the graph y = f(x) are; (0, 0), (2, 4), and (4, 0)
The required graph to draw is y = 2·f(x) - 3
Which gives;
(0, 2×0 - 3) = (0, -3)
(2, 2×4 - 3) = (2, 5)
(4, 2×0 - 3) = (4, -3)
The graph of the above data is plotted and included here
Learn more about transformation of functions here;
https://brainly.com/question/13976536
