Question

The point (14, -20 is on the graph of y = f(x). A point on the graph of y = g(x), where g(x) = f( - ) is a) A point on the graph of y = g(x), where g(x) = f(x + 15) is b) A point on the graph of y = g(x), where g(x) = 9f(2) is C) A point on the graph of y = g(x), where g(x) = f(x) - 6 is d) A point on the graph of y = g(x), where g(x) = – f(x) is e) A point on the graph of y= g(), where g(x) = f(a) is f)

Answer 1

The given point of y = f(x) is (14, - 20)

a) if a function, f(x) has a notation, f(- x), there is a reflection over the y axis. The sign of the y coordinate would remain the same while the sign of the x coordinate would change. Thus, it becomes

g(x) = f(-x) = (- 14, - 20)

b) g(x) = f(x + 15) means a horizontal movement, 15 units to the left. The coordinate would be (14 - 15, - 20)

= (- 1, - 20)

c) g(x) = 9f(x) is a vertical stretch of f(x) by 9 units. The new coordinates would be (14, 9 *- 20)

= (14, - 180)

d) g(x) = f(x) - 6 is a vertical translation down, 6 units. The new coordinate would be (14, - 20 - 6)

= (14, - 26)

e) g(x) = - f(x) is a reflection over the x axis. the sign of the x coordinate would remain the same while the sign of the y coordinate would change. Thus, it becomes

g(x) = f(-x) = (14, - - 20)

g(x) = (14, 20)

f) g = 1/2f(x) is a vertical compression by 1/2 units because 1/2 is less than 1. The coordinate would be

(14, 1/2 *- 20)

= (14, - 10)