ISEE Upper Level Quantitative Reasoning focuses on developing advanced mathematical skills and problem-solving abilities for high school students.
A function is a rule that assigns each input (often \( x \)) exactly one output (often \( y \)). Think of it as a vending machine: you put in a code (input), and you get a snack (output).
Functions can be shown visually on a coordinate plane. The most common is the straight line, represented by \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
By looking at graphs, you can see how changing one variable affects another. This is useful in science experiments, business, and even sports!
If you earn $5 per lawn mowed, the function \( y = 5x \) tells you how much you'll make for mowing \( x \) lawns. Graphing this helps you predict your earnings.
\[y = mx + b\]
Plot the points for \( y = 2x + 1 \) for \( x = 0, 1, 2 \): you get (0,1), (1,3), (2,5).
A graph showing temperature vs. time helps track how fast ice cream melts.
Functions and their graphs help us understand relationships between quantities.