If f(x) is a linear function which statement must be true? f(x) has no constant term. f(x) has no x^2 term. f(x) has no terms with a coefficient other than 1. f(x) has no x-term.

Question

Answer 1

To determine which statement must be true about the linear function \( f(x) \), let's first recall the general form of a linear function:

where:-

is the slope of the line,-

is the y-intercept, which is the constant term.A linear function is defined as a polynomial of degree 1, meaning it has the form

where

and

are constants and

.Now, let's analyze each statement:1. \( f(x) \) has no constant term. - This is not necessarily true. A linear function can have a constant term

.2. \( f(x) \) has no

-term. - This is true. A linear function does not include any

term because it is a polynomial of degree 1.3. \( f(x) \) has no terms with a coefficient other than 1. - This is not true. The coefficient

can be any real number, not just 1.4. \( f(x) \) has no x-term. - This is not true. A linear function must have an

-term (i.e., the term

).Given this analysis, the statement that must be true about a linear function \( f(x) \) is:

So, the correct answer is:

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