Answer:
- x ≤ 3
- y ≥ |x -2|
- y < 4 -|x -2|
Step-by-step explanation:
The vertical line at x=3 is the upper boundary of the area shaded to its left, where x < 3. The solid line indicates that x=3 is part of the solution. So, that inequality is ...
x ≤ 3
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The ∨-shaped pair of lines are created by an absolute value function. Its normal vertex of (0, 0) has been shifted to the right 2 units. The shift means the argument of the absolute value function will be (x-2). Shading is above the solid line(s), so y-values greater than or equal to those given by the absolute value function are part of the solution set.
y ≥ |x -2|
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The ∧-shaped pair of lines are created by an absolute value function that has been reflected across the x-axis. Its vertex has been moved to (2, 4), so the function is both vertically and horizontally shifted The dashed line means the function value is not part of the solution set, and the shading for y values less than the function value means the inequality is ...
y < -|x -2| +4
I like to write a difference with the minus sign between the terms. (Sometimes it gets lost if the leading sign is negative.)
y < 4 - |x -2|
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Comment on function transformations
Of course, you're well aware of the usual function transformations. For a parent function of f(x), the transformed function is ...
g(x) = (vertical scaling) × f(x - (horizontal right shift)) + (vertical shift up)
If the function has been reflected across the x-axis (is upside down), then the "vertical scaling" coefficient will be negative.
