Question

2. Consider the parent function f(x) = x. Which transformations occurred to create g(x) = -2]x-81+7?

2

a. vertical translation 7 units up
b. horizontal translation 8 units right
C. vertical translation 7 units down
d. reflection in the x-axis
c.horizontal translation 8 units left
f.reflection in y axis
g.vertical stretch by a factor of 2
h.horizontal stretch by a factor of 2

Answer 1

Answer: The transformations that occurred to create g(x) = -2(x-8)²-81+7 from f(x) = x are:

- Horizontal translation 8 units to the right: The term (x - 8) in the equation of g(x) means that the graph of g(x) has been shifted horizontally 8 units to the right compared to f(x) = x.

- Vertical stretch by a factor of 2: The coefficient -2 in front of the term (x - 8)² means that the graph of g(x) has been vertically stretched by a factor of 2 compared to f(x) = x.

- Vertical translation 81 units down and 7 units up: The terms -81 and +7 in the equation of g(x) mean that the graph of g(x) has been shifted vertically 81 units down and then 7 units up compared to f(x) = x.

Therefore, the correct answer is (a) vertical translation 7 units up.

Explanation: