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.

To determine which statement must be true about the linear function \( f(x) \), let's first recall the general form of a linear function:<br /><br />\[ f(x) = mx + b \]<br /><br />where:<br />- \( m \) is the slope of the line,<br />- \( b \) is the y-intercept, which is the constant term.<br /><br />A linear function is defined as a polynomial of degree 1, meaning it has the form \( ax + b \) where \( a \) and \( b \) are constants and \( a \neq 0 \).<br /><br />Now, let's analyze each statement:<br /><br />1. \( f(x) \) has no constant term.<br /> - This is not necessarily true. A linear function can have a constant term \( b \).<br /><br />2. \( f(x) \) has no \( x^2 \)-term.<br /> - This is true. A linear function does not include any \( x^2 \) term because it is a polynomial of degree 1.<br /><br />3. \( f(x) \) has no terms with a coefficient other than 1.<br /> - This is not true. The coefficient \( m \) can be any real number, not just 1.<br /><br />4. \( f(x) \) has no x-term.<br /> - This is not true. A linear function must have an \( x \)-term (i.e., the term \( mx \)).<br /><br />Given this analysis, the statement that must be true about a linear function \( f(x) \) is:<br /><br />\[ f(x) \text{ has no } x^2 \text{-term.} \]<br /><br />So, the correct answer is:<br /><br />\[ f(x) \text{ has no } x^2 \text{-term.} \]