1. **Match each equation with the description of the function it represents:** - a. $f(x) = 2x + 4$ - b. $g(x) = 2(x + 4)$ - c. $h(x) = 4x + 2$ - d. $k(x) = 4(x + 2)$ **Descriptions:** 1. Add 4 to input, then multiply by 2. 2. Add 2 to input, then multiply by 4. 3. Multiply input by 2, then add 4. 4. Multiply input by 4, then add 2. **Matching:** - a matches description 3 because $f(x) = 2x + 4$ means multiply input by 2, then add 4. - b matches description 1 because $g(x) = 2(x + 4)$ means add 4 to input, then multiply by 2. - c matches description 4 because $h(x) = 4x + 2$ means multiply input by 4, then add 2. - d matches description 2 because $k(x) = 4(x + 2)$ means add 2 to input, then multiply by 4. 2. **Function P represents the perimeter of a square with side length $x$ inches.** **a. Complete the table:** The perimeter of a square is given by the formula: $$P = 4x$$ Calculate $P(x)$ for each $x$: - $P(0) = 4 \times 0 = 0$ - $P(1) = 4 \times 1 = 4$ - $P(2) = 4 \times 2 = 8$ - $P(3) = 4 \times 3 = 12$ - $P(4) = 4 \times 4 = 16$ - $P(5) = 4 \times 5 = 20$ - $P(6) = 4 \times 6 = 24$ **Table:** | $x$ | 0 | 1 | 2 | 3 | 4 | 5 | 6 | |-----|---|---|---|---|---|---|---| | $P(x)$ | 0 | 4 | 8 | 12 | 16 | 20 | 24 | **b. Write an equation to represent function P:** $$P(x) = 4x$$ **c. Sketch a graph of function P:** The graph is a straight line passing through the origin $(0,0)$ with slope 4, showing that as side length $x$ increases, perimeter $P(x)$ increases by 4 times $x$. This completes the first problem fully.