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Compare the graph of the function ๐‘”(๐‘ฅ)=|๐‘ฅโˆ’1|+5๐‘”(๐‘ฅ)=|๐‘ฅโˆ’1|+5 to the graph of its parent function, ๐‘“(๐‘ฅ)=|๐‘ฅ|๐‘“(๐‘ฅ)=|๐‘ฅ|.Select all statements that apply to the transformation of ๐‘“(๐‘ฅ)๐‘“(๐‘ฅ) to ๐‘”(๐‘ฅ)๐‘”(๐‘ฅ).Question 8Select one or more:a.Vertical translation, down 55 unitsb.Vertical translation, up 55 unitsc.Vertical translation, down 11 unitd.Vertical translation, up 11 unite.Horizontal translation, left 55 unitsf.Horizontal translation, right 55 unitsg.Horizontal translation, left 11 unith.Horizontal translation, right 11 unit

Question

Compare the graph of the function ๐‘”(๐‘ฅ)=|๐‘ฅโˆ’1|+5๐‘”(๐‘ฅ)=|๐‘ฅโˆ’1|+5 to the graph of its parent function, ๐‘“(๐‘ฅ)=|๐‘ฅ|๐‘“(๐‘ฅ)=|๐‘ฅ|.Select all statements that apply to the transformation of ๐‘“(๐‘ฅ)๐‘“(๐‘ฅ) to ๐‘”(๐‘ฅ)๐‘”(๐‘ฅ).Question 8Select one or more:a.Vertical translation, down 55 unitsb.Vertical translation, up 55 unitsc.Vertical translation, down 11 unitd.Vertical translation, up 11 unite.Horizontal translation, left 55 unitsf.Horizontal translation, right 55 unitsg.Horizontal translation, left 11 unith.Horizontal translation, right 11 unit

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Solution

The function ๐‘”(๐‘ฅ)=|๐‘ฅโˆ’1|+5 is a transformation of the parent function ๐‘“(๐‘ฅ)=|๐‘ฅ|.

  1. The term (๐‘ฅโˆ’1) inside the absolute value function indicates a horizontal shift. Since it's (๐‘ฅ - 1), it means the graph of the function is shifted 1 unit to the right. So, option (h) "Horizontal translation, right 1 unit" applies.

  2. The "+5" outside the absolute value function indicates a vertical shift. Since it's "+5", it means the graph of the function is shifted 5 units up. So, option (b) "Vertical translation, up 5 units" applies.

Therefore, the transformations applied to the parent function ๐‘“(๐‘ฅ)=|๐‘ฅ| to get ๐‘”(๐‘ฅ)=|๐‘ฅโˆ’1|+5 are a horizontal shift 1 unit to the right and a vertical shift 5 units up.

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Similar Questions

Which function represents a horizontal translation of 55 units right and a vertical translation of 44 units up from the graph of ๐‘“(๐‘ฅ)=|๐‘ฅ|๐‘“(๐‘ฅ)=|๐‘ฅ|?Question 7Select one:a.๐‘”(๐‘ฅ)=|๐‘ฅ+5|+4๐‘”(๐‘ฅ)=|๐‘ฅ+5|+4b.๐‘”(๐‘ฅ)=|๐‘ฅโˆ’4|โˆ’5๐‘”(๐‘ฅ)=|๐‘ฅโˆ’4|โˆ’5c.๐‘”(๐‘ฅ)=|๐‘ฅ+4|+5๐‘”(๐‘ฅ)=|๐‘ฅ+4|+5d.๐‘”(๐‘ฅ)=|๐‘ฅโˆ’5|โˆ’4๐‘”(๐‘ฅ)=|๐‘ฅโˆ’5|โˆ’4e.๐‘”(๐‘ฅ)=|๐‘ฅ+5|โˆ’4๐‘”(๐‘ฅ)=|๐‘ฅ+5|โˆ’4f.๐‘”(๐‘ฅ)=|๐‘ฅโˆ’5|+4

Fill in the blanks to complete the statement:Compared to the graph of the parent function, ๐‘“(๐‘ฅ)=|๐‘ฅ|๐‘“(๐‘ฅ)=|๐‘ฅ|, the graph of ๐‘”(๐‘ฅ)=๐‘Ž|๐‘ฅ|๐‘”(๐‘ฅ)=๐‘Ž|๐‘ฅ|, where ๐‘Ž>1๐‘Ž>1, results in a vertical Answer 1 Question 11, making ๐‘”(๐‘ฅ)๐‘”(๐‘ฅ) Answer 2 Question 11 than the graph of ๐‘“(๐‘ฅ)๐‘“(๐‘ฅ).

What is the effect on the graph of the function f(x)=4x๐‘“(๐‘ฅ)=4๐‘ฅ when f(x)๐‘“(๐‘ฅ) is replaced with f(x+5)๐‘“(๐‘ฅ+5)?Question 9Select one:Translate vertically 5 units up.Translate vertically 5 units down.Translate horizontally 5 units right.Translate horizontally 5 units left.

Which statements describe one of the transformations performed on ๐‘“(๐‘ฅ)=๐‘ฅ2f(x)=x 2 to create ๐‘”(๐‘ฅ)=(๐‘ฅโˆ’2)2+5g(x)=(xโˆ’2) 2 +5? Choose all that apply.A.A translation of 5 units upB.A translation of 2 units to the leftC.A translation of 2 units to the rightD.A translation of 5 units downSUBMITarrow_backPREVIOUS

Instructions: Based on the information given in the problem, select the accurate transformation.What is the effect on the graph of the function f(x)=4(3)x๐‘“(๐‘ฅ)=4(3)๐‘ฅ when f(x)๐‘“(๐‘ฅ) is replaced with f(x)+7๐‘“(๐‘ฅ)+7?Translate Answer 1 Question 7 77 units Answer 2 Question 7CheckQuestion 7

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