Final answer:
In mathematics, a function represents a unique relationship between inputs and outputs, where each input corresponds to exactly one output. Functions can be represented algebraically, graphically, in tables, or verbally. Manipulating the slope or intercept of a function's equation will alter its graphical representation.
Step-by-step explanation:
What is a function in Mathematics?
A function is a special type of relationship in mathematics where each input is associated with exactly one output. The input is usually referred to as the independent variable, and the output is called the dependent variable.
Different ways to represent a function
Algebraically: A function can be represented using an equation. For example, the equation y = 2x + 1 is a function where the output y is determined by the input x.
Tabular: Functions can be represented in a tabulated form, with two columns, one for the input and one for the output.
Verbally: Sometimes functions are explained using words, as in 'The temperature T in Celsius is a function of the temperature in Fahrenheit F, where T = (5/9)(F - 32)'.
Manipulating Functions
To manipulate a function, you can change its defining equation, which in turn will alter its graph. Changing the slope or the intercept will tilt the line or move it up and down on the graph, respectively.