Question

Given the functions f(x) = x3 + x2 – 3x + 4 and g(x) = 2x – 4, 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 first function is a type of cubic function and second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The function given in the problem is:

f(x) = x³ + x² – 3x + 4

The highest degree (power) of this function is 3. Thus, this function is a type of cubic function.

The second function given in the problem is:

g(x) = 2x – 4

The highest degree (power) of this function is 1. Thus, this function is a type of linear function.

Both the function has the value of domain and range from -∞ to ∞ (-∞,∞).

Thus, the first function is a type of cubic function and second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).

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