The graphs of two functions, $f$ and $g$, are shown on the grid below - Junior Cycle Mathematics - Question 14 - 2015

Function: $f(x)$

Explanation: I identified $f(x)$ as the parabola because quadratic functions produce U-shaped graphs. In contrast, $g(x)$ as a linear function corresponds to a straight line. Thus, by analyzing the shape of the graphs, I matched them correctly.

$f(2)$ is found by following the $x$-value of 2 on the graph and reading vertically downwards to find the corresponding $y$-value. In this case, $f(2) = -3$.

Calculating:

$f(2) = (2)^2 - 2(2) - 3$

$= 4 - 4 - 3 = -3$

To find $x$ such that $g(x) = 3$, I locate the line $g(x)$ on the vertical line at $y = 3$ and find the intersection point. This occurs when $x = 2$.

For this equation, I set the two graphs equal to each other and find their points of intersection. This is satisfied at the points $(-1, 0)$ and $(4, 5)$, thus, $x = -1$ and $x = 4$.