The transformation that converts the graph of f(x)=5|x–2|+6 into the graph of g(x)=5|x+7|+6 is a horizontal shift.

Here are the steps to understand this:

1. Look at the function f(x)=5|x–2|+6. The |x–2| part of the function means that the graph is shifted 2 units to the right from the basic absolute value function f(x)=|x|.

2. Now look at the function g(x)=5|x+7|+6. The |x+7| part of the function means that the graph is shifted 7 units to the left from the basic absolute value function f(x)=|x|.

3. Comparing the two functions, we can see that the graph has been shifted from 2 units to the right to 7 units to the left.

So, the transformation that converts f(x) into g(x) is a horizontal shift of 9 units to the left.

Question

The transformation that converts the graph of f(x)=5|x–2|+6 into the graph of g(x)=5|x+7|+6 is a horizontal shift.

Here are the steps to understand this:

1. Look at the function f(x)=5|x–2|+6. The |x–2| part of the function means that the graph is shifted 2 units to the right from the basic absolute value function f(x)=|x|.

2. Now look at the function g(x)=5|x+7|+6. The |x+7| part of the function means that the graph is shifted 7 units to the left from the basic absolute value function f(x)=|x|.

3. Comparing the two functions, we can see that the graph has been shifted from 2 units to the right to 7 units to the left.

So, the transformation that converts f(x) into g(x) is a horizontal shift of 9 units to the left.

Knowee AI · Accepted Answer

The transformation that converts the graph of f(x)=5|x–2|+6 into the graph of g(x)=5|x+7|+6 is a horizontal shift.

Here are the steps to understand this:

1. Look at the function f(x)=5|x–2|+6. The |x–2| part of the function means that the graph is shifted 2 units to the right from the basic absolute value function f(x)=|x|.

2. Now look at the function g(x)=5|x+7|+6. The |x+7| part of the function means that the graph is shifted 7 units to the left from the basic absolute value function f(x)=|x|.

3. Comparing the two functions, we can see that the graph has been shifted from 2 units to the right to 7 units to the left.

So, the transformation that converts f(x) into g(x) is a horizontal shift of 9 units to the left.

What kind of transformation converts the graph of f(x)=5|x–2|+6 into the graph of g(x)=5|x+7|+6?

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