Chapter 1 - Functions and Their Graphs - Section 1.1 Functions - 1.1 Assess Your Understanding - Page 55: 83

$A=-3.5$

It is given, that $f(2)=5$. By substituting $x=2$ into the given function, and knowing that $f(2)=5$, then: $f(2)=2(2)^3+A(2)^2+4(2)-5$ $5=2(8)+A(4)+8-5$ $5=16+4A+8-5$ $5=19+4A$ Solving this equation fro $A$ we get: $5-19=4A$ $-14=4A$ $-\frac{14}{4}=A$ $-3.5=A$