Question

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice therainbow is the shape of a parabola.The equation for this parabola is y = -x + 271. In the distance, an airplane is taking off. As it ascends during take-off, it makes aslanted line that cuts through the rainbow at two points. Create a table of at least fourvalues for the function that includes two points of intersection between the airplaneand the rainbow.Linear function:1. Analyze the two functions. Answer the following reflection questions in completesentences2. What is the domain and range of the rainbow?3. Explain what the domain and range represent in context.4. Do all of the values make sense in this situation? Why or why not?5. What are the X- and y-intercepts of the rainbow?

Answer 1

Given: The equation of the rainbow has a shape of a parabola:

`y=-x^2+27`

In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points

We will draw a line that will be intersected with the parabole at two points and one of them has x = 4

See the following picture:

As shown in the figure, the plane takes off from the point (-18, 0)

And it makes a slanted line that cuts through the rainbow at two points.

The equation of the linear function will be: y = 0.5x + 9

The table of the linear function will be as follows:

2. What is the domain and range of the rainbow?

Domain = all the possible value of x = ( -∞, ∞ )

Range = all the possible value of y = ( -∞ , 27 )

3. Explain what the domain and range represent in context.

The domain is all the possible values of x that can be substituted into the function

So, as we have a polynomial function, the domain will be all real numbers

The range is all the possible values of y that will be results when we have substituted with the x-values

As we have a parabola, the range will be ( -∞ , 27 )

What are the X- and y-intercepts of the rainbow?

As shown in the figure:

There are two points:

`\begin{gathered} (4,11) \\ (-4.5,6.75) \end{gathered}`