How has the function below been transformed from the parent function f(x)=x2

Question

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g(x) = −(x+1)2+5


(2 points)
Yes No
g(x) shifted right 1 unit.

g(x) was reflected across the y-axis.

g(x) was reflected across the x-axis.

g(x) shifted down 5 units.

g(x) shifted left 1 unit.

g(x) shifted up 5 units.

Answer 1

To analyze how the function \( g(x) = -(x+1)^2 + 5 \) has been transformed from the parent function \( f(x) = x^2 \), we need to recognize how each transformation applies:

1. Horizontal Shift: The term \( (x + 1) \) indicates a horizontal shift. The plus sign with \( x \) means the graph is shifted left. Specifically, it shifts left 1 unit.

   • Conclusion: \( g(x) \) shifted left 1 unit. (Yes)

2. Reflection: The negative sign in front of the squared term, \( -(x+1)^2 \), indicates a reflection across the x-axis.

   • Conclusion: g(x) was reflected across the x-axis. (Yes)

3. Vertical Shift: The \( +5 \) at the end indicates a vertical shift upward. Specifically, it shifts the graph up 5 units.

   • Conclusion: g(x) shifted up 5 units. (Yes)

Summary of the Transformations:

• g(x) shifted right 1 unit: No
• g(x) was reflected across the y-axis: No
• g(x) was reflected across the x-axis: Yes
• g(x) shifted down 5 units: No
• g(x) shifted left 1 unit: Yes
• g(x) shifted up 5 units: Yes

Overall, the correct responses would be:

• g(x) shifted left 1 unit: Yes
• g(x) shifted right 1 unit: No
• g(x) was reflected across the y-axis: No
• g(x) was reflected across the x-axis: Yes
• g(x) shifted down 5 units: No
• g(x) shifted up 5 units: Yes