Question

Compared to its "parent" function f(x) = x², which of the following best describes the function f(x) = 2x² - 1?

(a) f(x) is stretched vertically by a factor of 2.
(b) f(x) is shifted upwards by 1 unit.
(c) f(x) is shifted downwards by 1 unit.
(d) f(x) is stretched vertically by a factor of 2 and shifted upwards by 1 unit.
(e) f(x) is stretched vertically by a factor of 2 and shifted downwards by 1 unit.

Answer 1

The function f(x) = 2x² - 1 is obtained from the parent function f(x) = x² by stretching vertically by a factor of 2 and shifting downwards by 1 unit.

Step-by-step explanation:

The function f(x) = 2x² - 1 is obtained from the parent function f(x) = x² by stretching vertically by a factor of 2 and shifting downwards by 1 unit. This means that the graph of f(x) = 2x² - 1 will be narrower and lower than the graph of f(x) = x².

To see this, compare the values of f(x) = x² and f(x) = 2x² - 1 for various x-values. For example, if you plug in x = 1 in both functions, you get f(1) = 1² = 1 for f(x) = x², and f(1) = 2(1)² - 1 = 2 - 1 = 1 for f(x) = 2x² - 1.

Therefore, the correct answer is (e) f(x) is stretched vertically by a factor of 2 and shifted downwards by 1 unit.