Questions: Write an equation of the function (g(x)) that is the graph of (f(x)=x), but shifted right 4 units and shifted up 8 units.

Write an equation of the function (g(x)) that is the graph of (f(x)=x), but shifted right 4 units and shifted up 8 units.
Transcript text: Write an equation of the function $g(x)$ that is the graph of $f(x)=|x|$, but shifted right 4 units and shifted up 8 units. $\square$ Submit Question
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Solution

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Solution Steps

Step 1: Horizontal Shift

To shift the graph of $f(x) = |x|$ horizontally by 4 units, we replace $x$ with $(x - (4))$ in the function. This gives us the intermediate function $g(x) = |x - (4))|$.

Step 2: Vertical Shift

To shift the graph vertically by 8 units, we add 8 to the function after applying the horizontal shift. This results in the final function $g(x) = |x - (4))| + (8).$

Final Answer:

The equation of the function after applying both horizontal and vertical shifts is $g(x) = |x - 4| + 8.$ This represents the graph of $f(x) = |x|$, shifted horizontally by 4 units and vertically by 8 units.

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