If the solid line models the function f(x) = |x^2| what is the equation of the transformed function (dotted line) which vertically stretched the starting function by a factor of 3

Question

Solid line points (0,0), (2,4) ,(-2,4)
Dotted line points (0,0), (1,4),((-1,4)
Options
f(x)= x^2-3
f(x) = x^2 +3
f(x) = 3|x^2|
f(x) = |(x +3)^2|

Answer 1

To transform the function \( f(x) = |x^2| \) by vertically stretching it by a factor of 3, we multiply the entire function by 3.

This gives us:

\[ g(x) = 3|x^2| \]

Now, we can compare this with the provided options:

1. \( f(x) = x^2 - 3 \)
2. \( f(x) = x^2 + 3 \)
3. \( f(x) = 3|x^2| \)
4. \( f(x) = |(x + 3)^2| \)

The correct equation of the transformed function, which vertically stretches the original function by a factor of 3, is:

\[ \boxed{f(x) = 3|x^2|} \]