Graphing a cube root function

Question

Graph the function.

Plot five points on the graph of the function, as follows.

1. Plot the first point using the x-value that satisfies 
2. Plot two points to the left and two points to the right of the first point.

Answer 1

I think I read your instructions correctly, but I will show how to graph the function, ƒ(x) = (³√x) - 6, by finding where it crosses the y-axis and then choosing two points to the right and left of that point.

(1) Find where f(x) crosses the y-axis by plugging in x = 0 into the function.

f(x) = (³√(0)) - 6 = - 6. : the cubed root of 0 is just 0, so 0 - 6 = - 6, thus the functions crosses the y-axis at

(0, -6)

(2) pick two points to the right of the previous coordinate, and two to the left.

Since we already found a coordinate for x = 0, let's use the x-values of -8, -1, 1, and 8 to keep the numbers simple and whole. Let's put everything into a table to make it easier to see.

x. y.

-8

-1

0 -6

1

8

(3) Plug in each value in the top row into the function to get the y-value.

I won't carry out each calculation, but here is a sample - solving for x = -8:

f(x) = (³√(-8)) - 6 = -8 : when x = -8, y = - 8. Do this same thing for the other x-values in the table using a calculator.

(4) Here is the full table filled out:

x. y.

-8 -8

-1 -7

0 -6

1 -5

8 -4

(5) Now that you have all of the x and y-values, simply plot them on a coordinate plane!

Desmos is a great tool for visualizing graphs of functions.