JEOPARDY Functions Linear Models Exponential Models Quadratic Models Miscellaneous 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4

1 Functions For the relation below, state the domain, range, and whether it is a function. ANSWER

1 Functions ANSWER Domain: {-2, -1, 0, 4} Range: {0, 2, 4, 5} Function? Yes, because for all ordered pairs (x,y), each value of x is paired with exactly one value of y. Jeopardy

2 Functions For the relation below, state the domain, range, and whether it is a function. ANSWER

2 Domain: all real numbers Range: {y: y ≤ -10 or y ≥ 10} Functions ANSWER Domain: all real numbers Range: {y: y ≤ -10 or y ≥ 10} Function? No, because it fails the vertical-line test for a function. Jeopardy

3 Functions For a set of data, the correlation coefficient r is -0.9 and the line of best fit is y = mx + b. Which of the following is a true statement? m > 0 m < 0 m can be any real number This is a weak correlation. ANSWER

3 Functions ANSWER B Jeopardy

4 Graph y = g(x) on the domain -5 ≤ x ≤ 5. Functions Graph y = g(x) on the domain -5 ≤ x ≤ 5. Find the range of g if the domain is the set of all real numbers. Give the x-intercepts of the graph of g. ANSWER

4 Functions ANSWER a. {y: y ≤ } There are no x-intercepts. Jeopardy

1 Linear Models Write an equation for the line that passes through (-6, 8) and (3, -1) in slope-intercept form. ANSWER

1 Linear Models ANSWER y = -1x + 2 Jeopardy

The values range from ___ to ___. 2 Linear Models A measure of the strength of a linear relation between two variables is the _______________________. The values range from ___ to ___. ANSWER

correlation coefficient 2 Linear Models ANSWER correlation coefficient -1 ≤ r ≤ 1 Jeopardy

3 Linear Models ________ of r indicates the _______ of the relation between the variables. _________ indicates the __________ of the relation. Perfect correlation in a situation where r = ___. ANSWER

3 Linear Models ANSWER SIGN of r indicates the DIRECTION of the relation between the variables. MAGNITUDE indicates the STRENGTH of the relation. Perfect correlation in a situation where r = ± 1. Jeopardy

4 Linear Models The table below gives the percent of the U.S. population who had completed at least four years of college for selected years. Find an equation for the line of best fit for these data. Let the independent variable be the number of years after 1900. Use your model from part a to estimate the percent of the U.S. population in 1994 who completed at least four years of college. What is the error of your estimate in part b? ANSWER

4 Linear Models ANSWER y = 0.19x – 1.42 Approx. 16.4% 1.3% Jeopardy

1 Exponential Models ANSWER

1 Exponential Models ANSWER f (0, 1) As x increases, f(x) approaches 0 and g(x) increases without bound. As x decreases, g(x) approaches 0 and f(x) increases without bound. Jeopardy

2 Exponential Models ANSWER

a. approx. 36.4% b. about 2.64 billion Exponential Models ANSWER a. approx. 36.4% b. about 2.64 billion Jeopardy

3 Exponential Models Suppose you purchased a car 20 years ago for $15,200. The value of the car decreased by 6% each year. What is the value of the car today? ANSWER

3 Exponential Models ANSWER $4,409.61 Jeopardy

4 Exponential Models A certain substance has a half life of 24 years. If a sample of 90 grams is being observed, how much will remain in 50 years? When will only 5 grams remain? ANSWER

4 Exponential Models ANSWER 21.24 grams 100 years Jeopardy

1 If a<0, a parabola has a ___________ point. Quadratic Models If a<0, a parabola has a ___________ point. If a>0, a parabola has a ___________ point. ANSWER

1 Quadratic Models ANSWER maximum, minimum Jeopardy

2 Quadratic Models The table below gives the percent of the U.S. population who had completed at least four years of college for selected years. Use the points (10, 2.7), (40, 4.6) and (70, 11.9) to find a quadratic model for these data. The independent variable represents the number of years after 1900. Use the quadratic model to predict the percent of the U.S. population having completed four years of college in the year 2010. ANSWER

2 Quadratic Models ANSWER y = 0.003x² - 0.086x + 3.27 30.03% Jeopardy

3 Quadratic Models Suppose a ball is hit upward from a height of 1 meters with an initial velocity of 35 meters per second. Find the relation between height h and time t after the ball is hit. How high is the ball after 3 seconds? ANSWER

3 Quadratic Models ANSWER a. b. 61.9 meters Jeopardy

4 Let f(x) = 2x² + x – 15. Find the y-intercept of f(x). Quadratic Models Let f(x) = 2x² + x – 15. Find the y-intercept of f(x). Find the x-intercepts of f(x). Tell whether the graph has a maximum or minimum point and find its coordinates. ANSWER

4 (0, -15) (5/2, 0) and (-3, 0) minimum at (-1/4, -121/8) Quadratic Models ANSWER (0, -15) (5/2, 0) and (-3, 0) minimum at (-1/4, -121/8) Jeopardy

1 Miscellaneous Order the scatterplots shown below in increasing order of correlation coefficient. ANSWER

1 Miscellaneous ANSWER C, B, D, A Jeopardy

2 Miscellaneous Evaluate f(n-2) if f(x) = 2x2 - 4 ANSWER

2 Miscellaneous ANSWER 2n2 - 8n + 4 Jeopardy

y varies inversely as the cube of x 3 Miscellaneous y varies inversely as the cube of x Suppose that y=10 when x=5. Find y when x=10. ANSWER

3 Miscellaneous ANSWER y = 1.25 Jeopardy

4 Miscellaneous Below are graphed the residuals for both the linear and quadratic models. What do these graphs tell you about the appropriateness of each model? ANSWER

4 Miscellaneous ANSWER The residuals for the linear model are positive at both ends, indicating that a better model can be found. The residuals for the quadratic model fall within a horizontal band centered around zero, so the quadratic model is a good fit. Jeopardy