1. The problem asks to match each function with the correct rule describing the sequence. 2. Let's analyze each function: - $f(x) = 5x + 2$: This is a linear function where the term $5x$ means multiply $x$ by 5, and then add 2. - $g(x) = 3 \cdot 4^x$: This is an exponential function with base 4, multiplied by 3. The sequence multiplies by 4 each step. - $h(x) = \frac{1}{2^x}$: This is an exponential decay function, dividing by 2 each step, or equivalently multiplying by $\frac{1}{2}$. - $m(x) = \frac{x+1}{2}$: This function adds 1 to $x$ and then divides by 2, which is equivalent to adding $\frac{1}{2}$ when considering the sequence increment. 3. Matching rules: - $f(x) = 5x + 2$ matches "add 5" (since multiplying $x$ by 5 and adding 2 is closest to adding 5 in the context of sequences). - $g(x) = 3 \cdot 4^x$ matches "multiply by 4" (exponential growth by factor 4). - $h(x) = \frac{1}{2^x}$ matches "multiply by 1/2" (each term is half the previous). - $m(x) = \frac{x+1}{2}$ matches "add 1/2" (adding 1 then dividing by 2 is equivalent to adding 0.5 in sequence terms). Final pairs: - $f(x) = 5x + 2$: add 5 - $g(x) = 3 \cdot 4^x$: multiply by 4 - $h(x) = \frac{1}{2^x}$: multiply by 1/2 - $m(x) = \frac{x+1}{2}$: add 1/2 This completes the matching of functions to rules.