I am not sure how to use the secant method formula without a function being given?

Question

Calculate an approximation value for $4^{\frac34}$ using four steps of the secant method with the starting values of $x_0=3$ and $x_1=2$.

Answer 1

You need to construct a function $f(x)$ such that $f(4^{\frac 34})=0$. There are many of those. One simple one is $f(x)=x- 4^{\frac 34}$. As Daniel Fischer suggests, another is $f(x)=x^4-64$. These will suggest others. The important thing is that the root be where you want and that the function be smooth and not have local maxima/minima in the region of interest. They may make your iteration not behave properly.