Select the correct answer. Function m is nonlinear and m(4)=9 Which equation could represent function m? A m(x)=9 B. m(x)=x^2-7 C. m(x)=(2)/(3)x-2 D m(x)=sqrt (x)+1

To determine which equation could represent the nonlinear function \( m \) given that \( m(4) = 9 \), we need to evaluate each option at \( x = 4 \) and see which one results in \( m(4) = 9 \).<br /><br />A. \( m(x) = 9 \)<br /><br />For this option, \( m(4) = 9 \). This satisfies the condition, but the function is linear (a constant function), not nonlinear.<br /><br />B. \( m(x) = x^2 - 7 \)<br /><br />Calculate \( m(4) \):<br />\[ m(4) = 4^2 - 7 = 16 - 7 = 9 \]<br />This satisfies the condition \( m(4) = 9 \), and the function is nonlinear (quadratic).<br /><br />C. \( m(x) = \frac{2}{3}x - 2 \)<br /><br />Calculate \( m(4) \):<br />\[ m(4) = \frac{2}{3} \times 4 - 2 = \frac{8}{3} - 2 = \frac{8}{3} - \frac{6}{3} = \frac{2}{3} \]<br />This does not satisfy the condition \( m(4) = 9 \).<br /><br />D. \( m(x) = \sqrt{x} + 1 \)<br /><br />Calculate \( m(4) \):<br />\[ m(4) = \sqrt{4} + 1 = 2 + 1 = 3 \]<br />This does not satisfy the condition \( m(4) = 9 \).<br /><br />The correct answer is B. \( m(x) = x^2 - 7 \), as it is a nonlinear function and satisfies \( m(4) = 9 \).