The key feature that the function of f(x) and g(x) has in common is the domain.
What is the domain and range of a function?
The domain of a function is the set of input or argument values for which the function is valid and well defined. The range is the set of the dependent variable for which a function is defined.
From the given information, we are to find the domain, range, x-intercept, and, y-intercept of the given equation:
[tex]\mathbf{f(x) = -4^x+5}[/tex]
[tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex]
For [tex]\mathbf{f(x) = -4^x+5}[/tex];
The domain of a function [tex]\mathbf{-4^x+5}[/tex] has no undefined points or constraints. Thus, the domain is -∞ < x < ∞.
- The range f(x) < 5.
- The x-intercepts, when y is zero = [tex]\mathbf{(\dfrac{In(5)}{2In(2)},0)}[/tex]
- The y-intercepts; when x is zero = (0,4)
For [tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex]
The domain of a function [tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex] has no undefined points or constraints. Thus, the domain is -∞ < x < ∞.
- The range -∞ < f(x) < ∞.
- The x-intercepts, when y is zero = (-2.939, 0)
- The y-intercepts; when x is zero = (0,5)
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