Check the answers below, please
1) Since we have this linear function:
[tex]f(x)=-\frac{1}{3}x-4[/tex]
a) We can proceed to state the Domain, the set of inputs for this function as:
[tex]D=(-\infty,\infty)[/tex]
Since this Linear function does not have any restraint or discontinuity.
b) The Range, i.e. the set of outputs for this function will be defined for this function as:
[tex]R=(-\infty,\infty)[/tex]
c) The Zero, can be found algebraically by plugging f(x)=0
[tex]\begin{gathered} f(x)=-\frac{1}{3}x-4 \\ 0=-\frac{1}{3}x-4 \\ \frac{1}{3}x=-4 \\ x=-12 \end{gathered}[/tex]
d) Y-intercept is the point in the y-axis where the line intercepts it. Looking at the rule of the function, we can state the y-intercept as:
[tex]-4[/tex]
e) Slope, the measure of how steep a line of a function is, it's always the coefficient of x, in this case:
[tex]m=-\frac{1}{3}[/tex]
f) Type of slope. Since the slope is -1/3 , i.e. lesser than 0, then we can classify it as decreasing
g) Evaluating f(3):
[tex]\begin{gathered} f(x)=-\frac{1}{3}x-4 \\ f(3)=-\frac{1}{3}(3)-4 \\ f(3)=-1-4 \\ f(3)=-5 \end{gathered}[/tex]
h) The value of x, where f(x)= -4 Similarly to the previous item, we can plug into that f(x)= -4 like this:
[tex]\begin{gathered} f(x)=-\frac{1}{3}x-4 \\ -4=-\frac{1}{3}x-4 \\ -4+4=-\frac{1}{3}x-4+4 \\ -\frac{1}{3}x=0 \\ \mathbf{x=0} \end{gathered}[/tex]
i) The graph can be traced having the zero, the y-intercept the type of the slope we can plot this:
