Answer
a) The domain of the given function is $\left( -\infty ,\infty \right)$.
b) The range of the given function is $\left[ -3,\infty \right)$.
c) The x-intercepts of the given function are $4,-2$
d) The y-intercept of the given function is $-2$
e) For the given function, $f\left( -4 \right)=2$
Work Step by Step
(a)
The domain of a function is the set of all values of x for which the function is defined.
Now, it can be clearly seen from the given graph that the domain of the function is the set of all real numbers.
Hence, the domain is $\left( -\infty ,\infty \right)$.
(b)
The values which the function can have for the domain is defined as the range of the function.
Now, it can be clearly seen from the provided graph that the y-coordinates of the function range from –3 to $\infty $.
Hence, the range is $\left[ -3,\infty \right)$.
(c)
The points where the graph cuts the x-axis are called the x-intercepts of the function.
Now, it can be observed that the graph cuts the x-axis at $-4$ and $2$.
Hence, the x-intercepts are $4$ and $-2$.
(d)
The points where the graph cuts the y-axis are called the y-intercepts of the function.
Now, it can be observed that the graph cuts the y-axis at –2.
Therefore, the y-intercept is $-2$.
(e)
It can be observed that the graph has the y-coordinate of 2 at $x=-4$.
Therefore, the value of $f\left( -4 \right)$ is $2.$
