Question

cubic & cube root functions cubic & cube root functions unit test back to intro page given the graph, determine f(64). hint: determine the function first. (1 point) 32 8 4 16

Explanation:

Step1: Identify the function type

The graph passes through the origin \((0,0)\) and has a shape consistent with a cube root function. The general form of a cube root function is \(y = \sqrt[3]{x}\) or \(y = \sqrt[3]{ax}\). Let's check points. For example, when \(x = 1\), if the function is \(y=\sqrt[3]{x}\), \(y = 1\), but looking at the graph, maybe it's a square root? Wait, no, cube root can take negative x. Wait, the graph at \(x = 0\) is 0, and let's check another point. Wait, maybe it's a square root? Wait, no, square root has domain \(x\geq0\), but the graph has negative x. Wait, no, the left side is for negative x, but cube root of negative x is negative. Wait, maybe the function is \(y=\sqrt[3]{x}\)? Wait, no, let's check the options. Wait, the problem is to find \(f(64)\). Let's assume the function is \(y = \sqrt[3]{x}\)? No, wait, maybe it's a square root? Wait, no, 64's square root is 8, cube root is 4. Wait, let's re-examine. Wait, the graph: when x is 0, y is 0. Let's see the points. Suppose the function is \(y=\sqrt[3]{x}\)? No, wait, maybe it's \(y = \sqrt{x}\)? But \(\sqrt{x}\) is only for \(x\geq0\), but the graph has negative x. Wait, maybe the function is \(y=\sqrt[3]{x}\), but the left side is for negative x. Wait, but the options are 32, 8, 4, 16. Wait, 64's square root is 8, cube root is 4. Wait, let's check the function. Wait, maybe the function is \(y=\sqrt[3]{x}\)? No, 64's cube root is 4. Wait, let's see: if the function is \(y = \sqrt[3]{x}\), then \(f(64)=\sqrt[3]{64}=4\)? Wait, no, \(\sqrt[3]{64}=4\)? Wait, \(4^3 = 64\), yes. Wait, but maybe the function is \(y=\sqrt{x}\)? No, \(\sqrt{64}=8\). Wait, the graph: let's see the points. At x=0, y=0. At x=1, y=1? No, the graph's points: maybe the function is \(y = \sqrt[3]{x}\)? Wait, no, maybe it's a square root. Wait, the problem says "Cubic & Cube Root Functions" in the title. So it's a cube root function? Wait, no, cubic functions are \(y = x^3\), but the graph is increasing slowly, like a root function. Wait, cube root function \(y = \sqrt[3]{x}\) has a point at x=8, y=2; x=64, y=4. Wait, that makes sense. So \(f(x)=\sqrt[3]{x}\), then \(f(64)=\sqrt[3]{64}=4\)? Wait, no, \(4^3=64\), yes. Wait, but let's check the options. The options are 32, 8, 4, 16. So 4 is an option. Wait, maybe the function is \(y = \sqrt[3]{x}\), so \(f(64)=4\).

Step2: Calculate \(f(64)\)

Assuming the function is \(y = \sqrt[3]{x}\) (since it's a cube root function unit test), then \(f(64)=\sqrt[3]{64}\). We know that \(4^3 = 64\), so \(\sqrt[3]{64}=4\).

Answer:

4