Answer:
In the attached graph
Step-by-step explanation:
To graph the function chose the values of x when subtract 2 from them give perfect cube numbers (number can be put in the form a³)
∵ 8 can be put in the form of 2³
- Put x - 2 = 8 ⇒ add 2 to both sides
∴ x = 10
∵ -8 can be put in the form of -2³
- Put x - 2 = -8 ⇒ add 2 to both sides
∴ x = -6
∵ 27 can be put in the form of 3³
- Put x - 2 = 27 ⇒ add 2 to both sides
∴ x = 29
∵ -27 can be put in the form of -3³
- Put x - 2 = -27 ⇒ add 2 to both sides
∴ x = -25
∵ 0 can be put in the form of 0³
- Put x - 2 = 0 ⇒ add 2 to both sides
∴ x = 2
Lets find the corresponding values of f(x) for x = -25, -6, 2 , 10 and 29
∵ [tex]f(x)=\sqrt[3]{x-2}[/tex]
∵ x = -25
∴ [tex]f(-25)=\sqrt[3]{-25-2}=\sqrt[3]{-27}=-3[/tex]
∵ x = -6
∴ [tex]f(-6)=\sqrt[3]{-6-2}=\sqrt[3]{-8}=-2[/tex]
∵ x = 2
∴ [tex]f(2)=\sqrt[3]{2-2}=\sqrt[3]{0}=0[/tex]
∵ x = 10
∴ [tex]f(10)=\sqrt[3]{10-2}=\sqrt[3]{8}=2[/tex]
∵ x = 29
∴ [tex]f(29)=\sqrt[3]{29-2}=\sqrt[3]{27}=3[/tex]
Now lets plot the points on the graph paper
Look to the attached graph
(-25 , -3) , (-6 , -2) , (2 , 0) , (10 , 2) , (29 , 3)
The x-intercept is (2 , 0)
The y-intercept is (0 , -1.26)
