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Given the functions f(x) = x3 x2 – 2x 3 and g(x) = log(x) 2, what type of functions are f(x) and g(x)? justify your answer. what key feature(s) do f(x) and g(x) have in common? (consider domain, range, x-intercepts, and y-intercepts.)

Sagot :

The functions f(x) and g(x) are different functions

The function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common feature in both functions is their range

According to the statement

we have given that the some functions and we have to justify these functions.

The functions are given as:

f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2

This means that the function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common key features of the functions

To do this, we plot the graphs of both functions

From the attached graph, we have the following features:

Function f(x)

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y - intercept = 3

x - intercepts = -2.37

Function g(x)

Domain: x > 0

Range: -∞ < y < ∞

y - intercept = None

x - intercepts = 0.01

By comparing the key features above, we can conclude that the common features in both functions is their range.

The functions f(x) and g(x) are different functions

The function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common feature in both functions is their range

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