Determine if the function is linear, constant, or neither. Part 1 of 4 \[ h(x)=-\frac{4}{5 x}-1 \] linear constant neither linear nor constant Part 2 of 4 \( \square \) linear Check Save For Late

To determine whether the function \( h(x) = -\frac{4}{5x} - 1 \) is **linear**, **constant**, or **neither**, let's analyze its form. ### **Definition of Terms:** 1. **Linear Function:** - A function is **linear** if it can be expressed in the form \( h(x) = mx + b \), where \( m \) and \( b \) are constants. - The graph of a linear function is a straight line. 2. **Constant Function:** - A function is **constant** if it does not depend on \( x \) and can be written as \( h(x) = c \), where \( c \) is a constant. - The graph of a constant function is a horizontal line. ### **Analyzing \( h(x) = -\frac{4}{5x} - 1 \):** 1. **Presence of \( x \) in the Denominator:** - The term \( -\frac{4}{5x} \) involves \( x \) in the denominator, making the function a **rational function**. - Rational functions are generally **not linear** because they include terms like \( \frac{1}{x} \), \( \frac{x}{x} \) (which simplifies to a constant), or higher powers of \( x \) in the denominator. 2. **Dependence on \( x \):** - The function depends on \( x \) due to the \( \frac{1}{x} \) term, so it is **not constant**. ### **Conclusion:** Since \( h(x) \) includes a term with \( \frac{1}{x} \) and cannot be expressed in the form \( mx + b \), it is **neither linear nor constant**. **Answer:** The function \( h(x) = -\frac{4}{5x} - 1 \) is **neither linear nor constant**.