Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=2
Evaluate
y+2=21x+1
To find the x-intercept,set y=0
0+2=21x+1
Removing 0 doesn't change the value,so remove it from the expression
2=21x+1
Swap the sides of the equation
21x+1=2
Move the constant to the right-hand side and change its sign
21x=2−1
Subtract the numbers
21x=1
Multiply by the reciprocal
21x×2=1×2
Multiply
x=1×2
Solution
x=2
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Solve the equation
Solve for x
Solve for y
x=2y+2
Evaluate
y+2=21x+1
Swap the sides of the equation
21x+1=y+2
Move the constant to the right-hand side and change its sign
21x=y+2−1
Subtract the numbers
21x=y+1
Multiply by the reciprocal
21x×2=(y+1)×2
Multiply
x=(y+1)×2
Solution
More Steps

Evaluate
(y+1)×2
Apply the distributive property
y×2+2
Use the commutative property to reorder the terms
2y+2
x=2y+2
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Testing for symmetry
Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis
Not symmetry with respect to the origin
Evaluate
y−−2=21x−−1
To test if the graph of y+2=21x+1 is symmetry with respect to the origin,substitute -x for x and -y for y
−y+2=21(−x)+1
Multiplying or dividing an odd number of negative terms equals a negative
−y+2=−21x+1
Solution
Not symmetry with respect to the origin
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Rewrite the equation
Rewrite in polar form
Rewrite in standard form
Rewrite in slope-intercept form
r=−2sin(θ)−cos(θ)2
Evaluate
y+2=21x+1
Multiply both sides of the equation by LCD
(y+2)×2=(21x+1)×2
Simplify the equation
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Evaluate
(y+2)×2
Apply the distributive property
y×2+2×2
Use the commutative property to reorder the terms
2y+2×2
Multiply the numbers
2y+4
2y+4=(21x+1)×2
Simplify the equation
More Steps

Evaluate
(21x+1)×2
Apply the distributive property
21x×2+1×2
Simplify
x+1×2
Any expression multiplied by 1 remains the same
x+2
2y+4=x+2
Move the expression to the left side
2y+4−x=2
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
2sin(θ)×r+4−cos(θ)×r=2
Factor the expression
(2sin(θ)−cos(θ))r+4=2
Subtract the terms
(2sin(θ)−cos(θ))r+4−4=2−4
Evaluate
(2sin(θ)−cos(θ))r=−2
Solution
r=−2sin(θ)−cos(θ)2
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Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=21
Calculate
y−−2=21x−−1
Take the derivative of both sides
dxd(y+2)=dxd(21x+1)
Calculate the derivative
More Steps

Evaluate
dxd(y+2)
Use differentiation rules
dxd(y)+dxd(2)
Evaluate the derivative
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Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
dxdy+dxd(2)
Use dxd(c)=0 to find derivative
dxdy+0
Evaluate
dxdy
dxdy=dxd(21x+1)
Solution
More Steps

Evaluate
dxd(21x+1)
Use differentiation rules
dxd(21x)+dxd(1)
Evaluate the derivative
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Evaluate
dxd(21x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
21×dxd(x)
Use dxdxn=nxn−1 to find derivative
21×1
Any expression multiplied by 1 remains the same
21
21+dxd(1)
Use dxd(c)=0 to find derivative
21+0
Evaluate
21
dxdy=21
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Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=0
Calculate
y−−2=21x−−1
Take the derivative of both sides
dxd(y+2)=dxd(21x+1)
Calculate the derivative
More Steps

Evaluate
dxd(y+2)
Use differentiation rules
dxd(y)+dxd(2)
Evaluate the derivative
More Steps

Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
dxdy+dxd(2)
Use dxd(c)=0 to find derivative
dxdy+0
Evaluate
dxdy
dxdy=dxd(21x+1)
Calculate the derivative
More Steps

Evaluate
dxd(21x+1)
Use differentiation rules
dxd(21x)+dxd(1)
Evaluate the derivative
More Steps

Evaluate
dxd(21x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
21×dxd(x)
Use dxdxn=nxn−1 to find derivative
21×1
Any expression multiplied by 1 remains the same
21
21+dxd(1)
Use dxd(c)=0 to find derivative
21+0
Evaluate
21
dxdy=21
Take the derivative of both sides
dxd(dxdy)=dxd(21)
Calculate the derivative
dx2d2y=dxd(21)
Solution
dx2d2y=0
Show Solution
