The cubic function can be graphed using the function behavior and the points.
x 0 1 2 3 4
y 0 −4 −12 −18 −16
How to estimate the function of [tex]$f(x)=x^{3}-5x^{2}[/tex]?
Put x = 0.
Replace the variable x with 0 in the expression.
[tex]f(0)=(0)^3-5(0)^2[/tex]
Raising 0 to any positive power yields 0.
f(0) = 0 − 5⋅0
f(0) = 0
y = 0
Put x = 1.
Replace the variable x with 1 in the expression.
[tex]f(1)=(1)^3-5(1)^2[/tex]
f(1) = 1− 5⋅1
f(1) = −4
y = −4
Put x = 2.
Replace the variable x with 2 in the expression.
[tex]f(2)=(2)^3-5(2)^2[/tex]
[tex]f(2)=8-5(2)^2[/tex]
f(2) = 8 − 5⋅4
f(2) = −12
y = −12
Put x = 3.
Replace the variable x with 3 in the expression.
[tex]f(3)=(3)^3-5(3)^2[/tex]
f(3) = 27 − 45
f(3) = −18
y = −18
Put x = 4.
Replace the variable x with 4 in the expression.
[tex]f(4)=(4)^3-5(4)^2[/tex]
[tex]f(4)=64-5(4)^2[/tex]
f(4) = 64 − 5 ⋅16
f(4) = 64 − 80
f(4) = −16
y = −16
The cubic function can be graphed using the function behavior and the points.
x 0 1 2 3 4
y 0 −4 −12 −18 −16
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