Question

Graph the function. Plot 5 points on the graph of the function as follow

Answer 1

Given the following function:

`\text{ y = f\lparen x\rparen = }\sqrt[3]{x}\text{ + 6}`

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,

`\text{ f\lparen0\rparen = }\sqrt[3]{0}\text{ + 6 = 0 + 6 = 6}`

Point 1 : (0, 6)

At x = 1,

`\text{ f\lparen1\rparen = }\sqrt[3]{1}\text{ + 6 = 1 + 6 = 7}`

Point 2: (1, 7)

At x = 8,

`\text{ f\lparen8\rparen = }\sqrt[3]{8}\text{ + 6 = 2 + 6 = 8}`

Point 3: (8, 8)

At x = -1,

`\text{ f\lparen-1\rparen = }\sqrt[3]{-1}\text{ + 6 = -1 + 6 = 5}`

Point 4: (-1, 5)

At x = -8,

`\text{ f\lparen-8\rparen = }\sqrt[3]{-8}\text{ + 6 = -2 + 6 = 4}`

Point 5: (-8, 4)

Let's now plot the points and the graph of the function: