Question

Which equation is represented by the graph below?

Answer 1

Answer:

The equation that is represented by the graph below is:

$y=f(x)=e^x$

Step-by-step explanation:

The graph is a curve such that it has the following representations:

when x=0 it passes through 1.

and also when x → ∞ it goes to ∞

and when x → -∞ it goes to 0.

Hence the function that satisfies all these properties is:

$y=f(x)=e^x$

1)

The first function:

$y=f(x)=\log x$

is not defined at x=0

2)

the function $y=f(x)=\log (x+1)$

at x=0 gives the value:

$y=f(0)=\log 1=0$

which does not satisfies the value as in graph.

3)

The function $f(x)=e^x$

satisfies all of the above properties.

4)

The function:

$y=f(x)=e^x+1$

at x=0 gives:

$f(0)=e^0+1=1+1=2$

which does not satisfies the point on the graph.

Hence, option 3) is correct.

$y=f(x)=e^x$ is the desired function.

Answer 2

let's proceed to graph each case to get the answer

using a graph tool

case a) $y=ln x$

see the attached figure N 1

The equation is not represented by the graph

case b) $y=ln x+1$

see the attached figure N 2

The equation is not represented by the graph

case c) $y=e^{x}$

see the attached figure N 3

The equation is represented by the graph ------> Is the solution

case d) $y=e^{x} +1$

see the attached figure N 4

The equation is not represented by the graph

therefore

the answer is

the equation is $y=e^{x}$