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Piecewise and Absolute Value FunctionsSelect the correct answer.Which function is represented by this graph?

Piecewise and Absolute Value FunctionsSelect the correct answer.Which function is-example-1
User Sachin Thapa
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1 Answer

17 votes
17 votes

Notice that the given graph is the graph of the function g(x)=|x| reflected over the x-axis, translated 1 unit to the right, and translated 1 unit up.

Now, recall that:

1) The function represented by the graph of the function h(x) reflected over the x-axis is:


-h(x)\text{.}

2) The function represented by the graph of the function h(x) translated n units to the right is:


h(x-n)\text{.}

3) The function represented by the graph of the function h(x) translated m units up is:


h(x)+m

Therefore, the function that is represented by the graph of g(x)=|x| reflected over the x-axis, translated 1 unit to the right, and then translated 1 unit up is:


f(x)=-|x-1|+1.

Answer: Second option.

User Flyingfromchina
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