Algebra 2 Honors/Gifted Around the Room on Functions

Question #1 Use the function graphed on the coordinate plane to the right. What are the intervals where the function is decreasing and increasing? The function decreases from (−∞,1) and increases from (1,∞) The function decreases from (2,∞) and increases from (−∞,2) The function decreases from (−∞,2) and increases from (2,∞) The function decreases from (1,∞) and increases from (−∞,1)

Question #2 Which of the following is true regarding the graph of 𝑓 𝑥 = 𝑥+1 −3? The graph has a vertex located at 1,−3 The graph has a y-intercept located at (0,2) The graph has a two x-intercepts located at (2,0) and (−4,0) The graph has a y-intercept located at (−2,0)

Question #3 The graph on the right shows the amount of money earned by Betsy’s babysitting business in one week. What is the domain of the function that best represents her money earned with respect to the number of hours she spent babysitting? All integers from 0 to 157 All integers from 0 to 15 All real numbers from 0 to 157 All real numbers from 0 to 15

Question #4 Which graph represents the function 𝑦= 𝑥−2 −3? a) b) c) d)

Question #5 Ms. Williams listed two functions, 𝑓 𝑥 and 𝑚(𝑥). She asked four of her students to list the solutions for the equation 𝑓 𝑥 =𝑚(𝑥). Their solutions are shown in the table below. Which student’s solution was correct? Mariah Riley Crystal Eva Name Conclusion Mariah It has 2 and 3 as its two solutions. Riley It has 1 and -2 as its two solutions. Crystal It has 4 and -3 as its two solutions. Eva It has 0 and -1 as its two solutions.

Question #6 What is the inverse of 𝑓 𝑥 = 3 4𝑥+1 ? 𝑓 −1 𝑥 = 3 4𝑦 − 1 4 𝑓 −1 𝑥 = 3 4𝑦 − 1 4 𝑓 −1 𝑥 = 3 4𝑥 − 1 4 𝑓 −1 𝑥 = 4𝑥+1 3 𝑓 −1 𝑥 = 1 4 − 3 4𝑥

Question #7 What is the average rate of change of 𝑓 𝑥 over the interval [−1,3]? 5 2 5 4 − 5 2

Question #8 Last year, a computer store sold 200 laptops at the price of $1,000 per laptop. The store manager is planning for the upcoming year. She creates the graph shown below of the projected revenue from the sales of laptop computers for next year depending on the price increase per laptop. What does the vertex of the parabola represent in terms of the context? The minimum revenue from laptops will be $2,000 when the price per laptop is not increased. The minimum revenue from laptops will be $200,000 when the price per laptop is not increased. The maximum revenue of $225,000 occurs when the laptops are priced at $1,500. The maximum revenue of $225,000 occurs when the laptops are priced at $500.

Question #9 Which graph illustrates the graphic representation for the daily sales of Wendy’s novel if the equation is 𝑠 =− 𝑥−7 +1000?

Question #10 What are the domain, range, relative maximum, and relative minimum for the function represented by the graph on the right? Domain = all real numbers; range = all real numbers; relative max = 4; relative min = 0 Domain = -2 to 2; range = all real numbers; relative max = 4; relative min = 0 Domain = all real numbers; range = all real numbers; relative max = 1; relative min = -1 Domain = all real numbers; range = -2 to 2; relative max = infinity; relative min = negative infinity

Answers: B C D A