Algebra
Calculus
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Question
Function
Evaluate the derivative
Find the domain
Find the x-intercept/zero
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y′={2x+52,x<32x−68,x>3
Evaluate
y=x2−8x−4∣x−3∣×15
Simplify
y=x2−8x−60∣x−3∣
Take the derivative of both sides
y′=dxd(x2−8x−60∣x−3∣)
Solution
y′={2x+52,x<32x−68,x>3
Show Solution
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=x2−8x−4∣x−3∣15
Simplify the expression
y=x2−8x−60∣x−3∣
To test if the graph of y=x2−8x−60∣x−3∣ is symmetry with respect to the origin,substitute -x for x and -y for y
−y=(−x)2−8(−x)−60∣−x−3∣
Simplify
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Evaluate
(−x)2−8(−x)−60∣−x−3∣
Calculate the absolute value
(−x)2−8(−x)−60∣x+3∣
Multiply the numbers
(−x)2+8x−60∣x+3∣
Rewrite the expression
x2+8x−60∣x+3∣
−y=x2+8x−60∣x+3∣
Change the signs both sides
y=−x2−8x+60∣x+3∣
Solution
Not symmetry with respect to the origin
Show Solution
Solve the equation
Solve for x
Solve for y
x∈(−∞,3)∩x=−856+y−26∪x∈(−∞,3)∩x=856+y−26∪x∈[3,+∞)∩x=−976+y+34∪x∈[3,+∞)∩x=976+y+34
Evaluate
y=x2−8x−4∣x−3∣×15
Simplify
y=x2−8x−60∣x−3∣
Swap the sides of the equation
x2−8x−60∣x−3∣=y
Move the expression to the left side
x2−8x−60∣x−3∣−y=0
Separate the equation into 2 possible cases
x2−8x−60(x−3)−y=0,x−3≥0x2−8x−60(−(x−3))−y=0,x−3<0
Solve the equation
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Evaluate
x2−8x−60(x−3)−y=0
Calculate
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Evaluate
x2−8x−60(x−3)−y
Expand the expression
x2−8x−60x+180−y
Subtract the terms
x2−68x+180−y
x2−68x+180−y=0
Add or subtract both sides
x2−68x=−180+y
Add the same value to both sides
x2−68x+1156=−180+y+1156
Simplify the expression
(x−34)2=976+y
Take the root of both sides of the equation and remember to use both positive and negative roots
x−34=±976+y
Separate the equation into 2 possible cases
x−34=976+yx−34=−976+y
Move the constant to the right-hand side and change its sign
x=976+y+34x−34=−976+y
Move the constant to the right-hand side and change its sign
x=976+y+34x=−976+y+34
x=976+y+34x=−976+y+34,x−3≥0x2−8x−60(−(x−3))−y=0,x−3<0
Solve the inequality
More Steps
Evaluate
x−3≥0
Move the constant to the right side
x≥0+3
Removing 0 doesn't change the value,so remove it from the expression
x≥3
x=976+y+34x=−976+y+34,x≥3x2−8x−60(−(x−3))−y=0,x−3<0
Solve the equation
More Steps
Evaluate
x2−8x−60(−(x−3))−y=0
Calculate
x2−8x−60(−x+3)−y=0
Calculate
More Steps
Evaluate
x2−8x−60(−x+3)−y
Expand the expression
x2−8x+60x−180−y
Add the terms
x2+52x−180−y
x2+52x−180−y=0
Add or subtract both sides
x2+52x=180+y
Add the same value to both sides
x2+52x+676=180+y+676
Simplify the expression
(x+26)2=856+y
Take the root of both sides of the equation and remember to use both positive and negative roots
x+26=±856+y
Separate the equation into 2 possible cases
x+26=856+yx+26=−856+y
Move the constant to the right-hand side and change its sign
x=856+y−26x+26=−856+y
Move the constant to the right-hand side and change its sign
x=856+y−26x=−856+y−26
x=976+y+34x=−976+y+34,x≥3x=856+y−26x=−856+y−26,x−3<0
Solve the inequality
More Steps
Evaluate
x−3<0
Move the constant to the right side
x<0+3
Removing 0 doesn't change the value,so remove it from the expression
x<3
x=976+y+34x=−976+y+34,x≥3x=856+y−26x=−856+y−26,x<3
Find the intersection
x∈[3,+∞)∩x=−976+y+34∪x∈[3,+∞)∩x=976+y+34x=856+y−26x=−856+y−26,x<3
Find the intersection
x∈[3,+∞)∩x=−976+y+34∪x∈[3,+∞)∩x=976+y+34x∈(−∞,3)∩x=−856+y−26∪x∈(−∞,3)∩x=856+y−26
Solution
x∈(−∞,3)∩x=−856+y−26∪x∈(−∞,3)∩x=856+y−26∪x∈[3,+∞)∩x=−976+y+34∪x∈[3,+∞)∩x=976+y+34
Show Solution
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