Question

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.)

Answer 1

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

The function types

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

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