Question

When the function f(x) = x^2 is multiplied by the value a, where a > 1, the graph of the new function, g(x) = ax^2, is:

a) Stretched vertically
b) Compressed vertically
c) Stretched horizontally
d) Compressed horizontally

Answer 1

The graph of the new function g(x) = ax^2, where a > 1, is stretched vertically.

Step-by-step explanation:

The graph of the new function g(x) = ax^2, where a > 1, is stretched vertically.

When a value greater than 1 is multiplied to the function f(x) = x^2, it causes the graph to become taller in relation to the x-axis. This is because the output values of g(x) will be greater than the corresponding output values of f(x).

For example, if we compare the graphs of f(x) = x^2 and g(x) = 2x^2, we will see that g(x) is taller than f(x) for the same x-values.