Using function concepts, it is found that the correct options are:
- Function g is positive over the interval [tex](-\infty, \infty)[/tex].
- The range of function g is [tex](3, \infty)[/tex].
- Function g has a y-intercept of (0,4).
What is the parent exponential function?
The parent exponential function is defined by:
[tex]y = e^x[/tex]
In this problem:
- When [tex]x = 0, e^x = 1[/tex], while [tex]g(x) = 4[/tex] when x = 0, hence it is 4 - 1 = 3 units above function f.
- From the graph, it is above the x-axis in the interval [tex](-\infty, \infty)[/tex], hence it is positive in this interval.
- The range is the set that contains all output values, that is, all values of y, hence it is [tex](3, \infty)[/tex].
- The domain is the set that contains all possible input values, hence it is [tex](-\infty, \infty)[/tex].
- The y-intercept is (0, g(0)), hence (0,4).
- Function g is increasing over the entire interval.
To learn more about function concepts, you can take a look at https://brainly.com/question/16948935
