1. The problem is to graph the function $f(x) = 4\sqrt{x} - 7$. 2. The formula used is $f(x) = 4\sqrt{x} - 7$, where $\sqrt{x}$ is the square root of $x$. 3. Important rules: - The square root function $\sqrt{x}$ is defined only for $x \geq 0$. - Multiplying by 4 stretches the graph vertically by a factor of 4. - Subtracting 7 shifts the graph down by 7 units. 4. To find key points, evaluate $f(x)$ at some values: - At $x=0$: $f(0) = 4\sqrt{0} - 7 = 0 - 7 = -7$ - At $x=1$: $f(1) = 4\sqrt{1} - 7 = 4 - 7 = -3$ - At $x=4$: $f(4) = 4\sqrt{4} - 7 = 4 \times 2 - 7 = 8 - 7 = 1$ 5. The graph starts at $(0, -7)$ and increases as $x$ increases, following the shape of the square root function but stretched and shifted. Final answer: The function $f(x) = 4\sqrt{x} - 7$ is defined for $x \geq 0$, starts at $(0, -7)$, and increases gradually as $x$ increases.