If f(x)=e^x, which of the following lines is an aymptote to the graph f

As x heads off to positive infinity, f(x) will do the same. This means f(x) grows without bound in the positive x direction. 

However, in the other direction, as x goes to negative infinity things are a bit different. Instead of going off to infinity, f(x) will approach y = 0. It will never touch or cross this horizontal line. It will only get closer and closer. Think of it as an electric fence you can't touch.

So there is only one horizontal asymptote and it is the horizontal line y = 0. This is the horizontal line that overlaps the x axis. 

Iam guessing c. or d.

and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

.

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .