Question

cubic & cube root functions cubic & cube root functions unit test back to intro page (0,0) (1,1) (8, 2) (-1, -1) -10 -5 5 10 -5 -10 give the 4 corresponding points that lie on the graph of g(x) = 4∛x. (4 points) (-1, -1) (1,1) (8,2) (0,0) (8,8) (0,0) (-1,3) (1,1) (0,4) (8,6) (2,8) (-1,-4) (1,4) (1,5)

Explanation:

Step1: Analyze the parent function

The original graph is of \( y = \sqrt[3]{x} \), with points \((-1, -1)\), \((0, 0)\), \((1, 1)\), \((8, 2)\) (since \( \sqrt[3]{-1}=-1 \), \( \sqrt[3]{0}=0 \), \( \sqrt[3]{1}=1 \), \( \sqrt[3]{8}=2 \)).

Step2: Apply the transformation \( g(x) = 4\sqrt[3]{x} \)

For a function transformation \( y = a\sqrt[3]{x} \), we multiply the \( y \)-coordinate of each point on \( y = \sqrt[3]{x} \) by \( a \) (here \( a = 4 \)).

For point \((-1, -1)\):

New \( y \)-coordinate: \( 4\times(-1)= -4 \), so the point is \((-1, -4)\).

For point \((0, 0)\):

New \( y \)-coordinate: \( 4\times0 = 0 \), so the point is \((0, 0)\).

For point \((1, 1)\):

New \( y \)-coordinate: \( 4\times1 = 4 \), so the point is \((1, 4)\).

For point \((8, 2)\):

New \( y \)-coordinate: \( 4\times2 = 8 \), so the point is \((8, 8)\).

Answer:

• Corresponding to \((-1, -1)\): \((-1, -4)\)
• Corresponding to \((0, 0)\): \((0, 0)\)
• Corresponding to \((1, 1)\): \((1, 4)\)
• Corresponding to \((8, 2)\): \((8, 8)\)