Question 138990
For a linear function the change in function, f(x), should be the same for each equal x division. 
In other words, when you go from -2 to -1, the change in the function should be the same as going from 0 to 1 and 2 to 3 and so on.
g(-2)-g(-1)=0.4444-1.333=-0.8889
g(1)-g(2)=12-36=-24
Definitely not the same, definitely not linear. 
Now look at f(x).
f(-2)-f(-1)=4-3.5=0.5
f(1)-f(2)=2.5-2=0.5
You can verify all of the other values to be sure. 
f(x) is a linear function. 
You can assume that g(x) is therefore the exponential function.
To be sure, you can do more analysis. 
Exponential functions have the form,
{{{g(x)=a*e^(bx)}}}
where a and b are constants.
{{{g(x+c)=a*e^(b(x+c))}}}
where c is a spacing constant, the distance between your x values.
Then you can look at the ratio of the values.
{{{g(x+c)/g(x)= e^(b(x+c))/e^(bx)}}}
{{{g(x+c)/g(x)= e^(bx+bc))/e^(bx)}}}
{{{g(x+c)/g(x)= e^(bx+bc-bx)}}}
{{{g(x+c)/g(x)= e^(bc)}}}
So, if your function is exponential, the ratio of two terms equals the same number.
g(-2)/g(-1)=0.4444/1.333=0.3333
g(1)/g(2)=12/36=0.3333
You can verify all of the other values to be sure. 
g(x) is an exponential function.