A vertical stretch of a function \( f(x) \) by a factor of \( k \) is achieved by multiplying the function by \( k \). In your case, the function you want to stretch vertically by a factor of 5 is \( f(x) = x^2 \).
To obtain the new function, you would multiply \( f(x) = x^2 \) by 5:
\[ g(x) = 5 \cdot f(x) = 5 \cdot x^2 = 5x^2 \]
So, the function that represents a vertical stretch of 5 of the graph of \( f(x) = x^2 \) is:
\[ g(x) = 5x^2 \]
1 answer