t(x)=x3+3×2-36x-108

Replace the variable x with -3 in the expression.

f(-3)=(-3)3+3(-3)2-36⋅-3-108

Simplify the result.

Simplify each term.

Raise -3 to the power of 3.

f(-3)=-27+3(-3)2-36⋅-3-108

Raise -3 to the power of 2.

f(-3)=-27+3⋅9-36⋅-3-108

Multiply 3 by 9.

f(-3)=-27+27-36⋅-3-108

Multiply -36 by -3.

f(-3)=-27+27+108-108

f(-3)=-27+27+108-108

Simplify by adding and subtracting.

Add -27 and 27.

f(-3)=0+108-108

Add 0 and 108.

f(-3)=108-108

Subtract 108 from 108.

f(-3)=0

f(-3)=0

The final answer is 0.

0

0

Convert 0 to decimal.

y=0

y=0

Replace the variable x with -2 in the expression.

f(-2)=(-2)3+3(-2)2-36⋅-2-108

Simplify the result.

Simplify each term.

Raise -2 to the power of 3.

f(-2)=-8+3(-2)2-36⋅-2-108

Raise -2 to the power of 2.

f(-2)=-8+3⋅4-36⋅-2-108

Multiply 3 by 4.

f(-2)=-8+12-36⋅-2-108

Multiply -36 by -2.

f(-2)=-8+12+72-108

f(-2)=-8+12+72-108

Simplify by adding and subtracting.

Add -8 and 12.

f(-2)=4+72-108

Add 4 and 72.

f(-2)=76-108

Subtract 108 from 76.

f(-2)=-32

f(-2)=-32

The final answer is -32.

-32

-32

Convert -32 to decimal.

y=-32

y=-32

Replace the variable x with -1 in the expression.

f(-1)=(-1)3+3(-1)2-36⋅-1-108

Simplify the result.

Simplify each term.

Raise -1 to the power of 3.

f(-1)=-1+3(-1)2-36⋅-1-108

Raise -1 to the power of 2.

f(-1)=-1+3⋅1-36⋅-1-108

Multiply 3 by 1.

f(-1)=-1+3-36⋅-1-108

Multiply -36 by -1.

f(-1)=-1+3+36-108

f(-1)=-1+3+36-108

Simplify by adding and subtracting.

Add -1 and 3.

f(-1)=2+36-108

Add 2 and 36.

f(-1)=38-108

Subtract 108 from 38.

f(-1)=-70

f(-1)=-70

The final answer is -70.

-70

-70

Convert -70 to decimal.

y=-70

y=-70

Replace the variable x with 0 in the expression.

f(0)=(0)3+3(0)2-36⋅0-108

Simplify the result.

Simplify each term.

Raising 0 to any positive power yields 0.

f(0)=0+3(0)2-36⋅0-108

Raising 0 to any positive power yields 0.

f(0)=0+3⋅0-36⋅0-108

Multiply 3 by 0.

f(0)=0+0-36⋅0-108

Multiply -36 by 0.

f(0)=0+0+0-108

f(0)=0+0+0-108

Simplify by adding zeros.

Add 0 and 0.

f(0)=0+0-108

Add 0 and 0.

f(0)=0-108

Subtract 108 from 0.

f(0)=-108

f(0)=-108

The final answer is -108.

-108

-108

Convert -108 to decimal.

y=-108

y=-108

Replace the variable x with 1 in the expression.

f(1)=(1)3+3(1)2-36⋅1-108

Simplify the result.

Simplify each term.

One to any power is one.

f(1)=1+3(1)2-36⋅1-108

One to any power is one.

f(1)=1+3⋅1-36⋅1-108

Multiply 3 by 1.

f(1)=1+3-36⋅1-108

Multiply -36 by 1.

f(1)=1+3-36-108

f(1)=1+3-36-108

Simplify by adding and subtracting.

Add 1 and 3.

f(1)=4-36-108

Subtract 36 from 4.

f(1)=-32-108

Subtract 108 from -32.

f(1)=-140

f(1)=-140

The final answer is -140.

-140

-140

Convert -140 to decimal.

y=-140

y=-140

The cubic function can be graphed using the function behavior and the points.

xy-30-2-32-1-700-1081-140

The cubic function can be graphed using the function behavior and the selected points.

Falls to the left and rises to the right

xy-30-2-32-1-700-1081-140

Graph t(x)=x^3+3x^2-36x-108