Given the following function:
[tex]\text{ y = f\lparen x\rparen = }\sqrt[3]{x}\text{ + 6}[/tex]
Let's determine 5 points that pass through its graph.
Since the function involves a cube root, let's use numbers that are perfect cubes to easily plot it.
Let's use x = 0, 1, -1, 8, -8
We get,
At x = 0,
[tex]\text{ f\lparen0\rparen = }\sqrt[3]{0}\text{ + 6 = 0 + 6 = 6}[/tex]
Point 1 : (0, 6)
At x = 1,
[tex]\text{ f\lparen1\rparen = }\sqrt[3]{1}\text{ + 6 = 1 + 6 = 7}[/tex]
Point 2: (1, 7)
At x = 8,
[tex]\text{ f\lparen8\rparen = }\sqrt[3]{8}\text{ + 6 = 2 + 6 = 8}[/tex]
Point 3: (8, 8)
At x = -1,
[tex]\text{ f\lparen-1\rparen = }\sqrt[3]{-1}\text{ + 6 = -1 + 6 = 5}[/tex]
Point 4: (-1, 5)
At x = -8,
[tex]\text{ f\lparen-8\rparen = }\sqrt[3]{-8}\text{ + 6 = -2 + 6 = 4}[/tex]
Point 5: (-8, 4)
Let's now plot the points and the graph of the function:
