# Graph f(x)=3x^5-2x^3+4x^2-6x+7

f(x)=3×5-2×3+4×2-6x+7
Find the point at x=-2.
Replace the variable x with -2 in the expression.
f(-2)=3(-2)5-2(-2)3+4(-2)2-6⋅-2+7
Simplify the result.
Simplify each term.
Raise -2 to the power of 5.
f(-2)=3⋅-32-2(-2)3+4(-2)2-6⋅-2+7
Multiply 3 by -32.
f(-2)=-96-2(-2)3+4(-2)2-6⋅-2+7
Multiply -2 by (-2)3 by adding the exponents.
Multiply -2 by (-2)3.
Raise -2 to the power of 1.
f(-2)=-96+(-2)(-2)3+4(-2)2-6⋅-2+7
Use the power rule aman=am+n to combine exponents.
f(-2)=-96+(-2)1+3+4(-2)2-6⋅-2+7
f(-2)=-96+(-2)1+3+4(-2)2-6⋅-2+7
f(-2)=-96+(-2)4+4(-2)2-6⋅-2+7
f(-2)=-96+(-2)4+4(-2)2-6⋅-2+7
Raise -2 to the power of 4.
f(-2)=-96+16+4(-2)2-6⋅-2+7
Raise -2 to the power of 2.
f(-2)=-96+16+4⋅4-6⋅-2+7
Multiply 4 by 4.
f(-2)=-96+16+16-6⋅-2+7
Multiply -6 by -2.
f(-2)=-96+16+16+12+7
f(-2)=-96+16+16+12+7
f(-2)=-80+16+12+7
f(-2)=-64+12+7
f(-2)=-52+7
f(-2)=-45
f(-2)=-45
-45
-45
Convert -45 to decimal.
y=-45
y=-45
Find the point at x=-1.
Replace the variable x with -1 in the expression.
f(-1)=3(-1)5-2(-1)3+4(-1)2-6⋅-1+7
Simplify the result.
Simplify each term.
Raise -1 to the power of 5.
f(-1)=3⋅-1-2(-1)3+4(-1)2-6⋅-1+7
Multiply 3 by -1.
f(-1)=-3-2(-1)3+4(-1)2-6⋅-1+7
Raise -1 to the power of 3.
f(-1)=-3-2⋅-1+4(-1)2-6⋅-1+7
Multiply -2 by -1.
f(-1)=-3+2+4(-1)2-6⋅-1+7
Raise -1 to the power of 2.
f(-1)=-3+2+4⋅1-6⋅-1+7
Multiply 4 by 1.
f(-1)=-3+2+4-6⋅-1+7
Multiply -6 by -1.
f(-1)=-3+2+4+6+7
f(-1)=-3+2+4+6+7
f(-1)=-1+4+6+7
f(-1)=3+6+7
f(-1)=9+7
f(-1)=16
f(-1)=16
16
16
Convert 16 to decimal.
y=16
y=16
Find the point at x=0.
Replace the variable x with 0 in the expression.
f(0)=3(0)5-2(0)3+4(0)2-6⋅0+7
Simplify the result.
Simplify each term.
Raising 0 to any positive power yields 0.
f(0)=3⋅0-2(0)3+4(0)2-6⋅0+7
Multiply 3 by 0.
f(0)=0-2(0)3+4(0)2-6⋅0+7
Raising 0 to any positive power yields 0.
f(0)=0-2⋅0+4(0)2-6⋅0+7
Multiply -2 by 0.
f(0)=0+0+4(0)2-6⋅0+7
Raising 0 to any positive power yields 0.
f(0)=0+0+4⋅0-6⋅0+7
Multiply 4 by 0.
f(0)=0+0+0-6⋅0+7
Multiply -6 by 0.
f(0)=0+0+0+0+7
f(0)=0+0+0+0+7
f(0)=0+0+0+7
f(0)=0+0+7
f(0)=0+7
f(0)=7
f(0)=7
7
7
Convert 7 to decimal.
y=7
y=7
Find the point at x=1.
Replace the variable x with 1 in the expression.
f(1)=3(1)5-2(1)3+4(1)2-6⋅1+7
Simplify the result.
Simplify each term.
One to any power is one.
f(1)=3⋅1-2(1)3+4(1)2-6⋅1+7
Multiply 3 by 1.
f(1)=3-2(1)3+4(1)2-6⋅1+7
One to any power is one.
f(1)=3-2⋅1+4(1)2-6⋅1+7
Multiply -2 by 1.
f(1)=3-2+4(1)2-6⋅1+7
One to any power is one.
f(1)=3-2+4⋅1-6⋅1+7
Multiply 4 by 1.
f(1)=3-2+4-6⋅1+7
Multiply -6 by 1.
f(1)=3-2+4-6+7
f(1)=3-2+4-6+7
Subtract 2 from 3.
f(1)=1+4-6+7
f(1)=5-6+7
Subtract 6 from 5.
f(1)=-1+7
f(1)=6
f(1)=6
6
6
Convert 6 to decimal.
y=6
y=6
Find the point at x=2.
Replace the variable x with 2 in the expression.
f(2)=3(2)5-2(2)3+4(2)2-6⋅2+7
Simplify the result.
Simplify each term.
Raise 2 to the power of 5.
f(2)=3⋅32-2(2)3+4(2)2-6⋅2+7
Multiply 3 by 32.
f(2)=96-2(2)3+4(2)2-6⋅2+7
Raise 2 to the power of 3.
f(2)=96-2⋅8+4(2)2-6⋅2+7
Multiply -2 by 8.
f(2)=96-16+4(2)2-6⋅2+7
Raise 2 to the power of 2.
f(2)=96-16+4⋅4-6⋅2+7
Multiply 4 by 4.
f(2)=96-16+16-6⋅2+7
Multiply -6 by 2.
f(2)=96-16+16-12+7
f(2)=96-16+16-12+7
Subtract 16 from 96.
f(2)=80+16-12+7
f(2)=96-12+7
Subtract 12 from 96.
f(2)=84+7
f(2)=91
f(2)=91
91
91
Convert 91 to decimal.
y=91
y=91
The 5th degree function can be graphed using the function behavior and the points.
xy-2-45-1160716291
The 5th degree function can be graphed using the function behavior and the selected points.
Falls to the left and rises to the right
xy-2-45-1160716291
Graph f(x)=3x^5-2x^3+4x^2-6x+7