Question

Use the graph of y = f(x) to graph the given function g.

g(x) = -2f(x)

Answer 1

I Think answer would be B

Answer 2

Why?

Answer 3

list down the coordinates for corners and endpoints of the graph with the solid line.
do the same with the dotted graph.
then for each x coordinate in each graph, compare the y coordinates...
which one of those choices is that the y coordinate in the solid graph -2 times as big as the y coordinate in the dotted graph?

Answer 4

b?

Answer 5

The negative sign in front of f(x) means that g(x) is going to reverse. The 2 means that every value of g is going to be double f.

Answer 6

g(x) = -2f(x), it's stating that the trace of the function g(x) is going to be flipped with respect to f(x) and elongated in the direction of the y-axis.

Answer 7

If I am understanding you correctly, I would choose D

Answer 8

That's what I would choose. If you look closely at D, you'll see that the trace of the dotted line g(f) is a slightly distorted "mirror image" reversal of the solid line f(x).
Each value of g(x) is double the value of the corresponding f(x), if you follow the x-values along the x-axis.

Answer 9

thanks

Answer 10

No problem, hope I wasn't overexplaining.
I think the key thing to remember is that the negative sign in front of the function gives you a symmetry across the x-axis.