A linear function is typically expressed in the form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. To determine which description can be represented as a linear function, let's analyze each option:
A. Eight more than twice a number: This can be expressed as \( f(x) = 2x + 8 \). This is a linear function.
B. Three more than the product of two numbers: This implies a multiplication of two variables, which typically results in a quadratic or more complex function. For example, if the numbers are \( x \) and \( y \), it could be expressed as \( f(x,y) = xy + 3 \), which is not a linear function.
C. Ten more than the square of a number: This can be expressed as \( f(x) = x^2 + 10 \). This is a quadratic function, not linear.
D. Nine more than one divided by a number: This could be expressed as \( f(x) = \frac{1}{x} + 9 \). The term \( \frac{1}{x} \) is a hyperbola, which is not linear.
Thus, the only description that can be written as a linear function is: A. Eight more than twice a number.