Final Answer:
The y-values of the two functions f(x) = 3x² - 3 and g(x) = 2ˣ - 3 differ significantly due to their distinct algebraic forms and behaviors.
Step-by-step explanation:
Firstly, let's analyze the function f(x) = 3x² - 3. This is a quadratic function, and the leading coefficient (3) indicates that the parabola opens upwards. The constant term (-3) shifts the parabola downward by three units. Thus, for any given x-value, the corresponding y-value will be the result of squaring x, multiplying by 3, and then subtracting 3.
Now, consider the function g(x) = 2ˣ - 3. This is an exponential function with a base of 2. Exponential functions grow (or decay) at a rate proportional to their current value. In this case, the term 2ˣ grows rapidly as x increases. The constant term (-3) shifts the entire graph downward by three units. Consequently, the y-values for g(x) will increase exponentially with increasing x.
In summary, while f(x) = 3x² - 3 represents a quadratic relationship resulting in a parabolic curve, g(x) = 2ˣ - 3 signifies exponential growth with a base of 2. The y-values of these functions diverge as they respond differently to changes in the input variable x, reflecting the distinctive characteristics of quadratic and exponential functions.