The y-values of the two functions f(x) = 3x² -3 and g(x) = 2* - 3 has the minimum y-value of g(x) approaches -3 and f(x) contains the smallest possible y-value.
It exists described as a special kind of relationship and they contain a predefined domain and range according to the function every value in the domain exists connected to just one value in the range.
Given: f(x) = 3x² -3
As we can see in the graph the first term exists 3x² and exists still positive for all x.
The range for f(x) ∈ [-3, ∞)
When x = 0 then f(x) = -3
The above value exists as the smallest possible value on the y-axis.
Given: Â [tex]g(x) = 2^x - 3[/tex]
[tex]2^x[/tex] exists also a positive quantity and it exists as an exponential function.
The range for the g(x) ∈ (-3, ∞)
It signifies that g(x) never touches the y-axis at -3.
We can express the minimum value of g(x) approaches -3.
Therefore, the correct answer is option B. The minimum y-value of g(x) approaches -3 and option D. f(x) has the smallest possible y-value.
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