What is the range of the function shown on the graph?

What's the smallest y can get? That would be y = -6; however, it does not actually get to -6. Instead it approaches to get closer and closer. This is due to the horizontal asymptote at y = -6.

What's the largest y can get? There is no upper bound. The y values grow forever because of the arrow indicating as such.

Therefore, the range is which written in interval notation would be

The range is all real numbers when y > -6

Step-by-step explanation:

The range is all real numbers when y > -6 because this includes all possible y-values that are greater than -6. This could go all the way up to infinity on the y-axis.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.