Pre-Calc Chapter 1 Sample Test. D) slope: 3 4

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1 Pre-Calc Chapter 1 Sample Test 1. Use the graphs of f and g to evaluate the function. f( x) gx ( ) (f o g)(-0.5) Plot the points and find the slope of the line passing through the pair of points. (, ), ( 4, 5) slope: 4 slope: 5 9 slope: 4 slope: 4 slope: 4. Evaluate the indicated function for f (x) = x + 4 and g (x) = x +. ( f g )(t + ) t + t + 9 t + 5t + t t + t + t + t + 5t Given x + y = 15, use the algebraic tests to determine symmetry with respect to both axes and the origin. x-axis, y-axis, and origin symmetry origin symmetry only no symmetry y-axis symmetry only x-axis symmetry only 5. Determine whether lines L 1 and L passing through the pairs of points are parallel, perpendicular, or neither. L 1 : (9, 6), ( 5, 4) L : (0, 9), ( 7, 4) parallel perpendicular neither

2 6. Find all real values of x such that f (x) = 0. f( x) = 64x ± 64 9 ± 64 8 ± 8 7. Assume that y is directly proportional to x. If x = and y = 4, determine a linear model that relates y and x. 4 y = x y = x y = x y = x y = x Which function does the graph represent?

3 9. Use the graph of to write an equation for the function whose graph is shown. 10. During math class, a fly lands on your graph paper. It lands at a point seven units from the left side of the paper and two units from the bottom of the paper. Before it flies away, it walks in a straight line to a point three units from the left side of the paper and ten units from the bottom of the paper. How far did the fly walk? Round to the nearest unit. 11 units 1 units 10 units 81 units 9 units 11. Find a mathematical model for the verbal statement: "w varies directly as the square of v and inversely as p." w kv p w= k vp = ( ) v w= k p p w= k v w= kv p

4 1. Use the graph of the function to find the domain and range of f. 1. Write the height h of the rectangle as a function of x.

5 14. The polygon is shifted to a new position in the plane. Find the coordinates of the vertices of the polygon in its new position. none of these 15. Find the domain of the function. 8w gw ( ) = w 6 all real numbers all real numbers w 6 all real numbers w 6, w 0 w = 6 w = 6, w = The graph shows the net profit (in thousands) for Deepti's landscaping business for the past year. Net profit (in thousands of dollars) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Use slopes to determine the month in which the net profit showed the greatest increase. February July September June January 17. Find the inverse function of f( x) = 7 x+ 5 x 5 gx= ( ) 7 1 gx ( ) = x 5 7 x gx= ( ) 5 x + 5 gx= ( ) 7 gx ( ) = 5 x 7

6 18. Find ( f / g )(x). f ( x) = x + 8x gx ( ) = 5 x x + 8 ( f / g)( x) =, x 0 5 x + 8x ( f / g)( x) =, x 5 5 x x ( f / g)( x) = 8, x 0 5 x + 8x ( f / g)( x) =, 5 x x 5 x + 8x ( f / g)( x) =, 5 x x Which equation does not represent y as a function of x? y = 7 + x x = y 4 y = x + 4 y = 6 + 8x x = 0. k After determining whether the variation model below is of the form y = kx or y =, find the value of x k. x y k = k = k = k = k = Determine whether the function has an inverse function. If it does, find the inverse function. f( x) = x + 1 f 1 ( x) = x + 1, x 0 No inverse function exists. f 1 ( x) = x 1 f 1 ( x) = x+ 1, x 6 f 1 ( x) = x 1. Use the position equation s = 16t + v 0 t + s 0 to write a function that represents the situation and give the average velocity of the object from time t 1 to time t. An object is thrown upward from a height of 100 feet at a velocity of 7 feet per second. t 1 = 1, t = 5 s= 16t + 7t+ 100 ; avg. velocity = 6 ft/s s= 16t + 100t+ 7 ; avg. velocity = 64 ft/s s= 16t + 7t+ 100 ; avg. velocity = 59 ft/s s= 16t + 7t+ 100 ; avg. velocity = 1 ft/s s= 16t + 100t+ 7 ; avg. velocity = 4 ft/s

7 . Find the distance between the points. Round to the nearest hundredth, if necessary. ( 5, 9), ( 4, ) Which graph represents the function? 5. x Use the functions given by f ( x ) = + 1 and 8 gx ( ) = x to find the indicated value. 1 g ( f ) (5) 6 undefined

8 6. Find ( f g )(x). 5x 5 f( x) = gx ( ) = 9 x x 5 x + 45 x+ 10 ( f g)( x) = 9 x x 5 x + 47 ( f g)( x) = 9 x 5 x + 45 x 10 ( f g)( x) = 9 x x 5 x + 4 ( f g)( x) = 9 x 5 x + 5 ( f g)( x) = 8 x 7. Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. f (x) = x + x + x + relative maximum: ( 1.58,.8) relative minimum: ( 0.4,.6) relative maximum: ( 0.4,.6) relative minimum: ( 1.58,.8) relative maximum: (.6, 46.6) relative minimum: (.8, 8.9) relative maximum: (.8, 1.58) relative minimum: (.6, 0.4) relative maximum: (.6, 0.4) relative minimum: (.8, 1.58) 8. Find the midpoint of the line segment joining the points. (9, ), ( 9, 8) (0, ) (, 0) (0, ) (9, 5) ( 5, 9) 9. Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope. point: ( 9, 8) slope: m = 5 y = 5x 9 y = 5x 1 y = 5x + 1 y = 5x + 7 y = 5x 8 0. Determine the quadrant(s) in which (x, y) is located so that the condition is satisfied. xy > 0 quadrant IV quadrant III quadrants II and IV quadrants I and III quadrant I

9 1. Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: (6, 1) line: 8x 40y = y = 5x + 9 y= x y = 8x y= x 8 4 y= 1 5 x+ 5. Determine the intervals over which the function is increasing, decreasing, or constant.. Find the zeroes of the functions algebraically. x 7 x 18 f( x) = 7x x = 9, x = x = 9, x = 1 x = 9, x =, x = x = 9, x =, 7 1 x = 7 1 x = 7

10 4. Describe the sequence of transformations from the related common function f ( x) = x to g. gx ( ) = x+ 8 reflection in the x-axis; then vertical shift 8 units down reflection in the y-axis; then horizontal shift 8 units right reflection in the y-axis; then vertical shift 8 units up reflection in the y-axis; then horizontal shift 8 units left reflection in the x-axis; then vertical shift 8 units up 5. Find g f. when f (x) = x + 5 g (x) = x ( g f)( x ) = x + 10x + 5 ( g f)( x ) = x + 5x + 5 ( g f)( x ) = x 5 ( g f)( x ) = x + 5 ( g f)( x ) = x Find the x- and y-intercepts of the graph of the equation y = x x. x-intercepts: ( 1,0), ( 0,0 ), ( 1,0 ); y-intercept: ( 0,0 ) x-intercepts: ( 0, 1), ( 0,0 ), ( 0,1 ); y-intercept: ( 0,0 ) x-intercepts: ( 1,0), ( 1,0 ); y-intercept: ( 0,0 ) x-intercepts: ( 1,0), ( 0,0 ), ( 1,0 ); y-intercepts: none x-intercepts: ( 0, 1), ( 0,1 ); y-intercept: ( 0,0 ) Determine the center and radius of the circle represented by the equation x+ + y = center:, 4 ; radius: 5 center:, 4 ; radius: center:, 4 ; radius: 9 5 center:, 4 4 ; radius: 5 center:, 4 ; radius:

11 8. The electrical resistance, R, of a wire is directly proportional to its length, l, and inversely proportional to the square of its diameter, d. A wire 100 meters long of diameter 5 millimeters has a resistance of 8 ohms. Find the resistance of a wire made of the same material that has a diameter of 1 millimeter and is 4 meters long. R = 0.15 ohms R = 10.5 ohms R = 11.5 ohms R = 8 ohms R = 11.8 ohms 9. Write the standard form of the equation of the circle whose radius is 9 and whose center is the point 6,5. ( ) ( x+ 6 ) + ( y+ 5) = 81 ( x ) ( y ) ( x 6 ) + ( y 5) = 9 ( x ) ( y ) ( x ) ( y ) = = = 81

12 40. Assuming that the graph shown has y-axis symmetry, sketch the complete graph.

13 Answer Key 1. D. E. D 4. A 5. A 6. E 7. E 8. C 9. E 10. E 11. A 1. A 1. E 14. B 15. D 16. D 17. A 18. B 19. E 0. B 1. D. C. D 4. D 5. C 6. C 7. A 8. A 9. D 0. E 1. A. D. A 4. E 5. A 6. A 7. A 8. E 9. E 40. B