Transformations of linear functions
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The parent function is \(f(x) = x\). Describe the transformation that produces each function and state the \(y\)-intercept of each.
(a) \(g(x) = x + 6\)
(b) \(h(x) = x - 4\)
(c) \(k(x) = x + 0\)
(a) \(g(x) = x + 6\): shifted 6 units up. \(y\)-intercept: \((0, 6)\).
(b) \(h(x) = x - 4\): shifted 4 units down. \(y\)-intercept: \((0, -4)\).
(c) \(k(x) = x\): no shift — this is the parent function. \(y\)-intercept: \((0, 0)\).
Adding a positive constant shifts up; subtracting shifts down. The slope is unchanged in all cases.
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