Which graph represents the function f(x)=−4x−3?

The graph on the top left.
f(x) = [tex]-4^x - 3[/tex]
That means that when x = 0...
f(0) = [tex]-4^0 - 3[/tex]
f(0) = -1 - 3
f(0) = -4
So, the function will have a point at (0, -4). We can eliminate the two graphs on the right.
When x = 1...
f(1) = [tex]-4^1 - 3[/tex]
f(1) = -4 - 3
f(1) = -7
So, the function will have a point at (1, -7). That corresponds to the graph on the top left.