Question

Let the graph of g be a translation 2 units left and 1 unit down, followed by a reflection in the y -axis of the graph of f(x)=(2x+1)^2-4 . Write a rule for g .

Answer 1

To write a rule for g, translate the function f(x) and reflect it in the y-axis.

Step-by-step explanation:

To write a rule for the graph g that involves translation and reflection, we can start with the rule for the original function f(x) = (2x+1)^2-4 and then apply the translation and reflection operations.

Translation 2 units left and 1 unit down: To translate a function 2 units left, we replace x with (x+2). To translate a function 1 unit down, we subtract 1 from the function. So the translation is: g(x) = ((2(x+2)+1)^2) - 4 - 1.

Reflection in the y-axis: To reflect a function in the y-axis, we replace x with -x. So the final rule for g is: g(x) = ((2(-x+2)+1)^2) - 4 - 1.