To determine which function is wider in each pair, we can compare the coefficients that determine the width of the parabolic curves.
a. Comparing y = x² and y = (20x)²:
- The function y = x² is wider because the coefficient of x² in the standard form is 1.
- In y = (20x)², the coefficient is 20² = 400, making it narrower.
b. Comparing y = x² and y = (1/5x)²:
- The function y = x² is wider with a coefficient of 1.
- In y = (1/5x)², the coefficient is (1/5)² = 1/25, making it narrower.
c. Comparing y = x² and y = (6x)²:
- The function y = x² is wider with a coefficient of 1.
- In y = (6x)², the coefficient is 6² = 36, making it narrower.
d. Comparing y = x² and y = (2/3x)²:
- The function y = x² is wider with a coefficient of 1.
- In y = (2/3x)², the coefficient is (2/3)² = 4/9, making it narrower.
In each case, the function with the smaller coefficient for x² is narrower, and the one with the coefficient of 1 (y = x²) is wider.