Let's analyze each statement individually. The first statement is
"Function g is positive on the interval (-∞, ∞)"
The function g has a horizontal asymptote at x = 3, and this is the minimum value this function can assume. Since 3 and all numbers above it are positive, the function g is indeed positive through all the real numbers and this statement is true.
The second statement is
"Function g is decreasing on the interval (-∞, 0)"
The function g is a translation of the parent exponential function, therefore, it has the same growth as the parent function, which is increasing through the entire domain. The second statement is false.
The third statement is
"The domain of function g is x > 0"
The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. Since the function is also defined for values smaller than zero(and also for zero), the third statement is false.
The fourth statement is
"Function g is 4 units above function f"
The horizontal asymptote of the parental function is y = 0. Since the horizontal asymptote here is y = 3, function g is 3 units above the parental function and the fourth statement is false.
The fifth statement is
"The range of function g is (3, ∞)"
The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs. This function assume the values above 3, therefore, the fifth statement is true.
Finally, the last statement is
"Function g has a y-intercept of (0, 4)"
The y-intercept is the point where the graph cuts the y-axis. This happens at (0, 4), therefore the last statement is also true.
The true statements are 1, 5 and 6.
