1. Which function is linear? \( f(x):(1,2),(2,6),(3,10),(4,14) \) \( g(x):(1,2),(2,4),(3,8),(4,16) \)

To determine which function is linear, we can look at the differences between the \( y \)-values for each function. For \( f(x) \), the differences are: \( 2-1 = 1 \), \( 6-2 = 4 \), \( 10-6 = 4 \), \( 14-10 = 4 \) (inconsistent differences). For \( g(x) \), the differences are: \( 2-1 = 1 \), \( 4-2 = 2 \), \( 8-4 = 4 \), \( 16-8 = 8 \) (also inconsistent). However, looking at the ratio of change in \( g(x) \), we notice it follows the pattern of \( 2^x \), so neither is linear. To verify, we can calculate the slope between points for \( g(x) \) which will show us the change isn’t constant—meaning it's quadratic. A real linear function would have constant differences (like \( f(x) \) increasing by 4 consistently). So, in summary, neither function is linear based on their growth patterns!