Which of the following could be an example of a function with a domain (-0,) and a range (-0,4)? Check all that apply.

Find the roots of the equation below. x^2 - 6 + 9 = 0

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. 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. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).

Solve the problem by using a venn diagram a group of students were surveyed about their taste in music. they were asked how they like three types of music: rock, country western and jazz. the results are summarized below: no one dislikes all three types of music. six like all three types of music. eleven don’t like country western. sixteen like jazz. three like country western and jazz, but not rock. six don’t like rock. eight like rock and country western. seven don’t like jazz. how many students were surveyed?