Question

VERY IMPORTANT

which series of transformations take the graph of f(x)=4x+9 to the graph of g(x)=-4x+7?

1. reflect the graph about the x axis and translate 2 units down?

2. reflect the graph about the y axis and translate 2 units up?

3. reflect the graph about the x axis and translate 2 units up?

4. reflect the graph about the y axis and translate 2 units down?

Answer 1

We start with   f(x)=4x+9.
Placing  a  " - " sign in front of the x term will reflect the graph of y=4x about the x-axis, but will not change the effect of that constant +9.
After this reflection your graph will still go through (0,9), but will have a slope of -4 instead of one of +4.

So, we'll end up with a line of slope m = -4 whose y-intercept is still (0,9).  Translating this graph downward by 2 units will result in the graph of 
y = -4x + 7.