WAEC Further Mathematics 2024 Paper

Concept:A small change in $y$, denoted $\Delta y$, is found using the change in $x$, denoted $\Delta x$, applied to the given linear function.Explanation:The function is $y = f(x) = 2x - 1$.An increase of $\Delta x = 0.1$ means the new value of $x$ is $x + 0.1$.Calculate the new value: $f(x + 0.1) = 2(x + 0.1) - 1$.Simplify: $f(x + 0.1) = 2x + 0.2 - 1$.So, $f(x + 0.1) = 2x - 1 + 0.2$.The original value is $f(x) = 2x - 1$.Therefore, $\Delta y = f(x + 0.1) - f(x)$.Substitute the expressions: $\Delta y = (2x - 1 + 0.2) - (2x - 1)$.Cancel the $2x$ and $-1$ terms: $\Delta y = 0.2$.Thus, the change in $y$ is $0.20$.Answer:$\Delta y = 0.20$, which corresponds to option A.