Explanation:
5.
just look at the table. what logic do you see in the change of the numbers ?
x changes by +1 from one point to the next.
y changes by +6 from one point to the next.
and we have the point with x=0 in the table, where y = 12. this is the y-intercept (where the line function crosses the y-axis, which means the point where x=0).
the changes line function is
y = ax + b
a is the slope. this is the ratio of y change / x change when going from one point to another.
in our case here this is 6/1 = 6.
b is the y-intercept. in our case 12.
so, the first equation is
y = 6x + 12
now, look at the second table.
x changes again by +1 from one point to the next.
y changes now by -3 from one point to the next.
so, our slope (a) here is -3/1 = -3.
we don't have the x=0 point in the table, so we get b by using the coordinates of one of the points (e.g. 2, 12) in the half finished equation and solve for b :
12 = -3×2 + b = -6 + b
18 = b
so, the full second equation is
y = -3x + 18
6.
this is totally simple. we put -3 in place of all x we find in the function definition and calculate the result :
f(-3) = (-3)³ + 27 = -27 + 27 = 0
remember that the exponent says how often the base number (here -3) is multiplied by itself. so, (-3)³ = -3×-3×-3.
-3×-3 = +9.
but then 9×-3 = -27.
7.
the domain of a function is the interval or set of valid values of x (the input variable).
remember, an empty dot means excluding, a filled dot means including.
I see the graph is drawn to go from x = -4 to x = +4.
-4 is included, +4 is excluded.
so, the domain is then the interval of the real numbers
[‐4, +4)
or
-4 <= x < +4
please consider that a round bracket means excluding.