The link between a function and its graph is really important in math. A function pairs each input (which we call an $x$-value) with just one output (called a $y$-value).

Key Points:

• What is a Function?: A function, written as $f(x)$, gives one special output for each input. For example, if we have $f(x) = 2x$, then:

  • When $x = 1$, $f(1) = 2$
  • When $x = 2$, $f(2) = 4$

• How is a Function Shown on a Graph?: A graph shows these input-output pairs as points on a grid. For our example, the graph for $f(x) = 2x$ will look like a straight line that goes through the starting point (the origin).

This line helps us see how $y$ changes when $x$ changes, making it easier to understand the function!

By looking closely at the graph, we can spot patterns and figure out how the function behaves. This is super helpful for understanding the math behind it!