Question

What is the effect on the graph of f(x) = x^2 when transformed to h(x) = (1/8)x^2 - 13?

Answer 1

The transformation of f(x) = x^2 into h(x) = (1/8)x^2 - 13 results in the graph being vertically compressed and shifted downward by 13 units, making the parabola wider and lower.

Step-by-step explanation:

The student's question asks about the effect of modifying the function f(x) = x^2 to the function h(x) = (1/8)x^2 - 13. There are two transformations to consider:

• The multiplication of the x^2 term by 1/8, which results in a vertical compression of the graph by a factor of 8. This means the parabola will be wider and less steep than the original f(x).
• The subtraction of 13 which translates the graph vertically downward by 13 units.

Thus, the transformed graph h(x) will be a wider parabola opening upwards, shifted downwards by 13 units on the y-axis, compared to the original graph of f(x).