The graph of the parent function, f(x) = x3, is translated such that the function g(x) = (x – 4)3 – 1 represents the new graph. Which transformations occurred? Horizontal translation: Vertical translation:

To determine which transformation changes the graph of \( f(x) = x^4 \) to the graph of \( g(x) = (x - 3)^4 - 2 \), we need to understand how transformations affect the graph of a function. 1. **Horizontal Translation**: - \( f(x - h) \) translates the graph of \( f(x) \) to the right by \( h \) units. - \( f(x + h) \) translates the graph of \( f(x) \) to the left by \( h \) units. 2. **Vertical Translation**: - \( f(x) + k \) translates the graph of \( f(x) \) up by \( k \) units. - \( f(x) - k \) translates the graph of \( f(x) \) down by \( k \) units. Given \( g(x) = (x - 3)^4 - 2 \): - The term \( (x - 3) \) indicates a horizontal translation to the right by 3 units. - The term \( -2 \) indicates a vertical translation down by 2 units. So, the correct transformation is: - Translate the graph of \( f(x) = x^4 \) to the right by 3 units. - Then translate it down by 2 units. This matches option **B**: - Translating it to the right by 3 units, then translating it down by 2 units. Therefore, the correct answer is **B**.

What kind of transformation converts the graph of f(x)=–|x–3|–9 into the graph of g(x)=–|x–4|+1?

What kind of transformation converts the graph of f(x)=4(x+7)2–2 into the graph of g(x)=4(x+1)2–4?translation 6 units left and 2 units downtranslation 6 units right and 2 units downtranslation 2 units right and 6 units uptranslation 2 units right and 6 units downSubmit

What kind of transformation converts the graph of f(x)=–8(x+4)2+1 into the graph of g(x)=–8(x+9)2+8?

What kind of transformation converts the graph of f(x)=5(x–8)2–1 into the graph of g(x)=5(x–5)2+5?translation 6 units left and 3 units uptranslation 3 units left and 6 units uptranslation 3 units right and 6 units downtranslation 6 units right and 3 units downSubmit