Answer
See the full explanation below.
Work Step by Step
(a)
The input values to the function are known as the domain of the function. In the graph, usually x-values are the input values to the function, the graph of which is plotted. Hence, the domain of the function denotes the x-values of the graph.
Hence, the domain of the function denote the x-values of the graph .
The graph of $f$ extends to $-\infty $ in the negative x-direction and to $6$ in the positive x-direction. So, the domain of f is given as,
$\left( -\infty ,6 \right]$
(b)
The values that are the output of the function are known as the range of the function. In the graph, usually y-values are the output values of the function, whose graph is plotted.
Hence, the y-values of the graph denote the range of the function.
The graph of $f$ extends to $-\infty $ in negative y-direction and to $1$ in positive y-direction.
So, the range of f is given as,
$\left( -\infty ,1 \right]$
(c)
The zeros of $f$ are the values of x for which the value of the function is zero. So, the zeros of the function f are at,
$\left( -\text{3,0} \right)$ and $\left( \text{3,0} \right)$
(d)
The value of $f\left( 0 \right)$ is the value of the function when $x=0$. So, the value is,
$f\left( 0 \right)=1$
(e)
The function is said to be increasing when the value of the function increase with the increase in x-values.
Thus, the value of the provided function increases on the interval $\left( -\infty ,-2 \right)$.
(f)
The function is said to be decreasing when the value of the function decreases with the increase in x-values.
Thus, the value of the provided function decreases on the interval $\left( 2,6 \right]$.
(g)
A function is constant if it does not change with the change in the variable. Thus, the value of the provided function remains constant on the interval $\left( -2,2 \right)$.
(h)
The value of the provided function $f\left( x \right)>0$ , that is, positive, is for the values of x which lie on the interval $\left( -3\text{,3} \right)$.
(i)
The value of the provided function has value $-2$ at approximately $x=-5\text{ and }x=5$.
(j)
The value of y is $-1$ when x is 4. So, the value of $f\left( 4 \right)$ is negative, that is, $f\left( 4 \right)=-1.$
(k)
If the graph of a function is symmetric about the y-axis, then it is an even function and if it is symmetric about the origin, then it is an odd function.
The graph of the provided function is symmetric neither about the y-axis nor about the origin.
So, the function is neither an even function nor an odd function.
(l)
The relative maximum of a function will be at that value of x at which y-value will be maximum as compared to all other points.
The value of provided function has maximum value at $x=2$. The maxima is $1$.
