Question

Which function grows at the fastest rate for increasing values of x?

h(x)=2x

f(x)=4x2+9x

g(x)=18x

Answer 1

Option 2. f(x) = 4x² + 9x

Explanation:

In this question we have to tell which function grows at the fastest rate for increasing values of x.

1) h(x) = 2x It's a linear function increasing with the value of x.

2). f(x) = 4x²+9x It's a function representing parabola. Moreover the value of the function increases exponentially as the function is in the form of quadratic equation.

3). g(x) = 18x it's again a linear function.

Therefore out of three functions Function 2 will grow at the fastest rate for increasing values of x.

Answer 2

When x gets large, the function of highest degree will always grow the fastest.

The blue curve (f(x)) may start out below the others, but quickly surpasses them.