Question 207963
If we let {{{f(x)=e^x}}}, then {{{h(x)=-f(x)=-e^x}}}. Recall that f(x) is used in place of 'y'. So what does {{{-f(x)}}} mean? It simply means {{{-y}}}. So what we're doing is taking EVERY y coordinate on the graph of {{{e^x}}} and negating it to get a y-coordinate on {{{-e^x}}}. Visually, we're reflecting the graph over the x-axis.



Here's the visual:


Graph of {{{f(x)=e^x}}}



{{{ drawing(500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,e^x)

)}}}



and the graph of {{{h(x)=-e^x}}}



{{{ drawing(500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,-e^x)

)}}}