# Functions and Straight Line Graphs

## Functions and Straight Line Graphs

# Understanding Functions

- A
**function**is a special relationship where each input has a single output. - It can be thought of as a machine which takes inputs (often denoted by ‘x’) and provides outputs (often denoted by ‘f(x)’ or ‘y’).
- It’s important to understand the difference between the
**input**(the value you feed into the function) and the**output**(the result you get out). - An example of a function is
*f(x) = 2x + 3*. In this case, for every x you input, the function will output a value that is double the input and then adds three.

# Deciphering Straight Line Graphs

**Understanding Graph Components**

- A straight line graph can be defined by the equation
*y = mx + c*, where m represents the**gradient**of the line and c represents the**y-intercept**. - The
**gradient**(m) defines the steepness of the line; a larger absolute value of m will result in a steeper line. - The
**y-intercept**(c) is where the line intersects with the y-axis.

**Plotting the Graph**

- To plot a straight line, you need at least two points. However, for higher accuracy, it’s recommended to plot more points.
- Choose some values of x and substitute them into the function to calculate the corresponding y-values.
- Plot these points (x, y) on a graph and draw the line that passes through these points.

**Interpreting the Graph**

- Once the graph is plotted, you can interpret it. If the line slopes upwards from left to right, this indicates a
**positive correlation**, and if it slopes downwards, this indicates a**negative correlation**. - The point where the line crosses the y-axis is the
**y-intercept**; this gives you the base value of the function when x=0. - You can also estimate the value of y for any given value of x by finding the corresponding point on the line.

**Working with Multiple Functions**

- When working with multiple functions, each function can be plotted on the same set of axes for comparison.
- This can help to solve problems like finding the intersection points of the functions (the values of x for which the functions are equal).

# Key Terms to Remember:

**Function**: a relationship between inputs and outputs**Gradient**: the slope or steepness of a line**Y-intercept**: the point where the line crosses the y-axis**Positive correlation**: when the graph slopes upwards from left to right**Negative correlation**: when the graph slopes downwards from left to right.