Let the graph of g be a translation 4 units down followed by a reflection in the y-axis of the graph of f(x)=x. Write a rule for g

Question

Let the graph of g be a translation 4 units down followed by a reflection in the y-axis of the graph of f(x)=x. Write a rule for g.

Answer 1

Let the graph of g be a translation of 4 units down followed by a reflection in the y-axis of the graph of f(x)=x. Write a rule for g.

Transformations can be found using this general formula: f(x) = a(bx-h)+k

For this question, we want a translation down as well as a reflection.

The two values we need to use are for k, a vertical translation, and b, a reflection over the y-axis.

Since we are translating down 4 units, k = -4

Since we are reflecting across the y-axis, b = -1

So, f(x)=(-x)-4

or

f(x) = -x - 4