Solve y = | 3|x| - 1

Question

Function

Evaluate the derivative

Find the domain

Find the x -intercept/zero

y^{'} = ⎩ ⎨ ⎧ - 3, x < - \frac{1}{3} 3, - \frac{1}{3} < x < 0 - 3, 0 < x < \frac{1}{3} 3, x > \frac{1}{3}

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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

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x \in (- \infty, 0) \cap x = - \frac{1 + y}{3} \cup x \in (- \infty, 0) \cap x = \frac{- 1 + y}{3} \cup x \in [0, + \infty) \cap x = \frac{1 + y}{3} \cup x \in [0, + \infty) \cap x = \frac{1 - y}{3}

Evaluate

y = ∣ 3 ∣ x ∣ - 1 ∣

Swap the sides of the equation

∣ 3 ∣ x ∣ - 1 ∣ = y

Separate the equation into 2 possible cases

3 ∣ x ∣ - 1 = y 3 ∣ x ∣ - 1 = - y

Solve the equation for x

More Steps

x \in (- \infty, 0) \cap x = - \frac{1 + y}{3} \cup x \in [0, + \infty) \cap x = \frac{1 + y}{3} 3 ∣ x ∣ - 1 = - y

Solve the equation for x

More Steps

x \in (- \infty, 0) \cap x = - \frac{1 + y}{3} \cup x \in [0, + \infty) \cap x = \frac{1 + y}{3} x \in (- \infty, 0) \cap x = \frac{- 1 + y}{3} \cup x \in [0, + \infty) \cap x = \frac{1 - y}{3}

Solution

x \in (- \infty, 0) \cap x = - \frac{1 + y}{3} \cup x \in (- \infty, 0) \cap x = \frac{- 1 + y}{3} \cup x \in [0, + \infty) \cap x = \frac{1 + y}{3} \cup x \in [0, + \infty) \cap x = \frac{1 - y}{3}

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