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

Answer 2

Solution:

The function is, f(x)= $-(x+1)^2$

It can be Written as, $(x+1)^2=-y$

The given equation is of Parabola, opening below , X axis.

The vertex of Parabola is , (-1 , 0).

Comparing with general equation of Parabola ,

$x^2=4 a y\\\\ 4 a = -1\\\\ a=\frac{-1}{4}$

The focus of the given parabola is obtained by, putting , x+1=0,gives, x=-1,So focus will be, $(-1,\frac{-1}{4})$

And equation of Directrix is, $y=\frac{1}{4}$

Line, x=-1, divides the parabola into two symmetrical Parts.