Question

F(x) = 2^x and G(x) = x; graph F-G

Answer 1

Given the two functions

`F(x)=2^x,G(x)=x_{}`

We are tasked to plot (F-G)(x).

The first step here is to get the resulting function (F-G)(x). We have

`(F-G)(x)=2^x-x`

Now, we need to assign values of x and evaluate them at the function (F-G)(x) to get a value. We will get coordinate points and we will plot them at the cartesian coordinate plane. I will use values of x = [-3,3]. We get the following results

`\begin{gathered} (F-G)(-3)=2^(-3)-(-3)=3.125\rightarrow\rightarrow(-3,3.125)_{}_{} \\ (F-G)(-2)=2^(-2)-(-2)=3.125\rightarrow\rightarrow(-2,2.25)_{} \\ (F-G)(-1)=2^(-1)-(-1)=3.125\rightarrow\rightarrow(-1,1.5)_{} \\ (F-G)(0)=2^0-0=1\rightarrow\rightarrow(0,1)_{} \\ (F-G)(1)=2^1-1=1\rightarrow\rightarrow(1,1)_{} \\ (F-G)(2)=2^2-2=2\rightarrow\rightarrow(2,2)_{} \\ (F-G)(3)=2^3-3=5\rightarrow\rightarrow(3,5)_{} \end{gathered}`

The plot is provided by the image below.