Question

Which function grows the fastest for large values of x? f(x)=8x f(x)=3x f(x)=4x2+3 f(x)=1.5x 20 points

Answer 1

The 4 functions are:
$f_1 (x) = 8x$
$f_2(x)=3x$
$f_3(x)=4x^2+3$
$f_4(x)=1.5 x$

Let's keep in mind that for large values of x, a quadratic function grows faster than a linear function:
$ax^2 \ \textgreater \ kx$ for large values of x

In this problem, we can see that the only quadratic function is $f_3(x)$, while all the others are linear functions, so the function that grows faster for large values of x is
$f_3(x) = 4x^2 +3$