Question

The graph of the function f(x) = –(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function.

Answer 1

A function
`f` from a set
`A` to a set
`B` is a relation that assigns to each element
`x` in the set
`A` exactly one element
`y` in the set
`B`. The set
`A` is the domain (also called the set of inputs) of the function and the set
`B` contains the range (also called the set of outputs).

The graph of a function
`f` is the collection of ordered pairs
`(x,f(x))` such that
`x` is in the domain of
`f` being:

`x` the directed distance from the
`y-axis`.

`y=f(x)` the directed distance from the
`x-axis`.

By plotting the function
`f(x)=-(x+1)^2` we get the graph illustrated below.

From this graph, we know that:

• The vertex is the maximum value
• The function is positive for no values of x
• The function is decreasing when
  `x>-1`
• The domain of the function is all real numbers
• The range of the function is all real numbers less or equal to 0