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It emphasizes pairing each input with exactly one output, identifying whether a question asks for values, rules, domains, or interpretation, and showing enough work. 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Make sure you show enough work for another student to follow your thinking.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do transformations work when changes happen inside versus outside f(x)?",{"text":117,"@type":113},"Changes outside the function directly affect all outputs, such as shifting the graph up or down. 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Pay attention to what the input means, what rule is being applied, and whether the question asks for a value, a rule, a domain, or an interpretation.  \n▷ Example: For f(x) = 2x + 5, 􀀂nd f (4) .  \nWork: Replace x with 4: f (4) = 2(4) + 5 = 13 .  \n⋆ Answer: 13  \n♦ Practice Problems  \nSolve each problem. Show enough work that another student could follow your thinking.  \n1. Describe g(x) = f (x) + 5 compared to f.  \n2. Describe g(x) = f (x) 􀀀 3 compared to f.  \n3. Describe g(x) = f (x + 2) compared to f.  \n4. Describe g(x) = f (x 􀀀 6) compared to f.  \n5. Describe g(x) = 􀀀f(x) compared to f.  \n6. Describe g(x) = f (􀀀x) compared to f.  \n7. Describe g(x) = 3f(x) compared to f.  \n8. Describe g(x) = 12f (x) compared to f.  \n9. If f(x) = x2 , write the rule for shifting it right 4 and up 1.  \n10. If f (x) = |x| has vertex (0 , 0), 􀀂nd the vertex of g (x) =|x + 3| 􀀀 2.  \n♦ Word Problems  \n11. A graph of f is shifted up 7 to make g. Write g in terms of f.  \n12. A parent graph f is re􀀃ected over the x-axis and shifted left 5. Write the new rule.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nAnswer Keys  \n1.  Shift up 5  7. Vertical stretch by 3  \n2.  Shift down 3  8. Vertical compression by 12  \n3.  Shift left 2  9.  g (x) = (x 􀀀 4)2 + 1   \n4.  Shift right 6  10.  (􀀀3, 􀀀2)   \n5.  Re􀀃ect over the x-axis  11. g (x) = f (x) + 7  \n6. Re􀀃ect over the y-axis 12. g (x) = 􀀀f(x + 5)  \nStep-by-Step Explanations  \n1. Adding 5 outside the function lifts every output, so the whole graph slides up by 5 units.  \n2. Subtracting outside takes away from every output, dragging the graph 3 units downward.  \n3. Changes inside the parentheses act in reverse: +2 moves the graph to the left, not the right.  \n4. Subtracting 6 inside makes the graph wait 6 extra units before doing what f would do—that’s a right shift.  \n5. A negative on the whole output 􀀃ips every y-value upside down, mirroring the graph across the x-axis.  \n6. Negating the input swaps left and right, so the graph re􀀃ects across the y-axis instead.  \n7. Multiplying the output by 3 pulls every point three times farther from the x-axis—a vertical stretch.  \n8. A factor between 0 and 1 outside squishes the graph toward the x-axis, soit’s a vertical compression.  \n9. Right shifts subtract inside, up shifts add outside—apply both to the parent x2 .  \n10. x + 3 inside moves the vertex 3 left, and 􀀀2 outside drops it 2 down.  \n11. An upward shift is an outside change, so the whole","cbCaiqBjuKleZhKl","https://ap.wps.com/l/cbCaiqBjuKleZhKl","pdf",101679,"English","# Quick Review and Helpful Hints\n# Practice Problems\n## Describe g(x) Compared to f\n## Word Problems\n# Answer Keys\n# Step-by-Step Explanations","[{\"question\":\"What should you pay attention to when solving function problems in this section?\",\"answer\":\"Focus on what the input means, what rule is applied, and whether the question asks for a value, a rule, a domain, or an interpretation. Make sure you show enough work for another student to follow your thinking.\"},{\"question\":\"How do transformations work when changes happen inside versus outside f(x)?\",\"answer\":\"Changes outside the function directly affect all outputs, such as shifting the graph up or down. Changes inside the parentheses act in reverse for horizontal shifts, so + inside moves left and - inside moves right.\"},{\"question\":\"What types of transformations are practiced here?\",\"answer\":\"The practice includes shifts (up, down, left, right), reflections over the x-axis and y-axis, and vertical transformations such as vertical stretch and compression using multipliers.\"}]","Graphing Functions and Transformations - PERT Math Section 4.4 - Practice Problems | PDF",1790672941]