f(x) = x^2 is the parent function.

Question

The value of k is 4.

On
 asheet of graph paper, sketch both y = f(x) and y = kf (x) for your
chosen parent function and chosen value of k. Be sure to clearly label each.

Answer 1

To graph the given functions based on the parent function \( f(x) = x^2 \) and the value \( k = 4 \):

1. Identify the parent function:
   The parent function is \( f(x) = x^2 \). This is a standard parabola that opens upwards with its vertex at the origin (0, 0).

2. Determine the new function:
   With \( k = 4 \), the new function is \( y = kf(x) = 4f(x) = 4x^2 \). This function is a vertical stretch of the parent function by a factor of 4.

3. Sketch both functions:

   • Plotting \( y = f(x) = x^2 \):

     • Points to plot:
       • (-2, 4)
       • (-1, 1)
       • (0, 0)
       • (1, 1)
       • (2, 4)

   • Draw a smooth curve through these points, creating the familiar U-shape for the parabola.

   • Plotting \( y = 4f(x) = 4x^2 \):

     • Points to plot:
       • (-2, 16)
       • (-1, 4)
       • (0, 0)
       • (1, 4)
       • (2, 16)

   • Draw a steeper curve through these points, also creating a U-shape, but opening more steeply than the parent function.

4. Label the graphs:

   • Label the graph of \( y = x^2 \) as "Parent Function: \( y = x^2 \)".
   • Label the graph of \( y = 4x^2 \) as "Transformed Function: \( y = 4x^2 \)".

Additional Notes:

• When graphing, make sure to plot enough points to accurately represent the shape of the parabolas.
• The transformed graph \( y = 4f(x) \) will reach higher values more quickly due to the vertical stretch.
• Ensure the axes are clearly labeled and scaled appropriately for both functions.

This setup would give you a visual representation of how the function \( y = 4x^2 \) stretches compared to the parent function \( y = x^2 \).