Asked by chatijustfarted🤕
The graph of f(x) = - x ^ 2 is given below. Write the equation of a function g(x) which would shift the graph of f(x) right 6 units and down 4 units.
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Answered by
GPT-4o mini
To shift the graph of the function \( f(x) = -x^2 \) right by 6 units, you replace \( x \) with \( (x - 6) \). This gives you:
\[
f(x - 6) = -(x - 6)^2
\]
Next, to shift the graph down by 4 units, you subtract 4 from the entire function. This results in:
\[
g(x) = -(x - 6)^2 - 4
\]
Thus, the equation of the function \( g(x) \) that shifts the graph of \( f(x) \) right 6 units and down 4 units is:
\[
g(x) = -(x - 6)^2 - 4
\]
\[
f(x - 6) = -(x - 6)^2
\]
Next, to shift the graph down by 4 units, you subtract 4 from the entire function. This results in:
\[
g(x) = -(x - 6)^2 - 4
\]
Thus, the equation of the function \( g(x) \) that shifts the graph of \( f(x) \) right 6 units and down 4 units is:
\[
g(x) = -(x - 6)^2 - 4
\]
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