Which function grows the fastest for large values of x?
f(x)=1.5x
f(x)=8x
f(x)=3x
f(x)=4x2+3
that makes no sense to me
I think the answer is f=1.5x
To determine which function grows the fastest for large values of x, we need to compare the growth rates of the functions. One way to do this is by analyzing the coefficients and exponents in each function.
Let's go through each function to see how they grow for large values of x:
1. f(x) = 1.5x
This function has a coefficient of 1.5 and an exponent of 1. As x gets larger, the function grows linearly. The growth rate is constant since the coefficient and exponent both remain the same.
2. f(x) = 8x
This function has a coefficient of 8 and an exponent of 1. Similar to the previous function, the growth remains linear, but the coefficient is larger. Therefore, this function grows faster than f(x) = 1.5x.
3. f(x) = 3x
This function has a coefficient of 3 and an exponent of 1. As with the previous two functions, the growth is linear, but the coefficient is smaller. Consequently, this function grows slower than f(x) = 8x but faster than f(x) = 1.5x.
4. f(x) = 4x^2 + 3
This function has an exponent of 2, which means it is quadratic. As x gets larger, the quadratic term (x^2) will dominate the growth of the function. Quadratic functions grow faster than linear functions for large values of x. Therefore, this function grows the fastest among the given options.
Thus, the function f(x) = 4x^2 + 3 grows the fastest for large values of x.
ax^2 grows faster than kx for any a and k you choose.
or, equivalently,
if a > b,
x^a grows faster than x^b