Question

Which equation is represented by the graph below?

Answer 1

Equation
`\rm \bold{y = e^x}` represents the graph shown in given figure.

Hence option (3) is the correct option.

The function given in the options of the figure are

`\rm (1) \; ln(x)\\ (2) \ln (x) +1\\(3)\; e^x \\(4) \; e^x +1 \\`

The graphs of all the options are attached below

The options (1) and (2) are logarithmic function and options (3) and (4) are exponential function

The addition of constant shifts the function upwards or downwards depending upon the sign of constant.

hence for
`\rm y = e^x +1`

The function
`\rm e^x` is shifted by 1 unit in +y direction.

Similarly we can conclude about the logarithmic function.

The graph shown in figure is similar to the function
`\rm y = e^x` hence option (3) is correct.

It can be seen that for
`\rm y = e^x` the y values are always positive and x values vary from
`\{ -\infty \; , \infty\}`.

So option (3) is the correct option.

Equation
`\rm \bold{y = e^x}` represents the graph shown in given figure.

For more information please refer to the link below

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)`