Practice Test - Chapter 2
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1 1 State the domain and range of the relation shown in the table Then determine if it is a function If it is a function, determine if it is one-to-one, onto, both, or neither 4 Write 2y = 6x + 4 in standard form Identify A, B and C The domain is the set of x-coordinates The range is the set of y-coordinates Since each element in the domain is related with unique element in the range, it is a function Since 2 and 6 are mapped to 3 in the range, the function is not one-to-one Since each element in the range has an element in the domain, the function is onto Compare the equation with the equation From the equation, A = 6, B = 2, C = 4 Because A, B, and C have a common factor of 2, divide each by 2 So, A = 3, B = 1, and C = 2 5 Find the x-intercept and the y-intercept for 3x 4y = 24 Substitute y = 0 in the equation Find each value if f (x) = 2x f ( 4) So, the x-intercept is ( 8, 0) Substitute x = 0 in the equation 3 f (3y) So, the y-intercept is (0, 6) esolutions Manual - Powered by Cognero Page 1
2 6 MULTIPLE CHOICE The cost of producing x pumpkin pies at a small bakery is given by C(x) = x Find the cost of producing 25 pies 8 ( 2, 7), (3, 1) A $7400 B $8150 C $9275 D $10825 Substitute x = 25 in the equation The slope of the line that passes through ( 2, 7) and (3, 1) is 9 MULTIPLE CHOICE Find the equation of the line that passes through (0, 3) and (4, 1) The cost of producing 25 pies is $9275 So, the correct choice is C Find the slope of the line that passes through each pair of points 7 (1, 6), (3, 10) F y = x + 3 G y = x 3 H y = x 3 J y = x + 3 The slope of the line that passes through (1, 6) and (3, 10) is 2 Substitute m = 1 and in the equation esolutions Manual - Powered by Cognero Page 2
3 10 Write an equation in slope-intercept form for the line that has slope 2 and passes through the point (3, 4) Substitute m = 2 and (x, y) = (3, 4) in the equation 12 Write an equation in slope-intercept form for the line that passes through ( 3, 5) and is parallel to y = 6x + 1 Since the required line is parallel to y = 6x + 1, the slope of the line is the same as the slope of the line y = 6x + 1 So, m = 6 Substitute m = 6 and (x, y) = ( 3, 5) in the slopeintercept form y = mx + b Substitute m = 2 and b = 6 in the formula So, the equation for the line that has slope 2 and passes through the point (3, 4) is 11 Write an equation of the line that passes through the points (2, 4) and (1, 6) Substitute m = 6 and b = 13 in the slope-intercept form y = mx + b So, the slope-intercept form for the line that passes through ( 3, 5) and is parallel to y = 6x + 1 is y = 6x EMERGENCY ROOM A hospital tracks the number of emergency room visits during the fall and winter months in the point- Substitute m = 10 and slope form a Make a scatter plot and describe the correlation b Use two ordered pairs to write a prediction equation c Use your prediction equation to estimate the number of emergency room visits for March a Make a scatter plot So, the equation of the line that passes through the points (2, 4) and (1, 6) is y = 10x + 16 Since the number of room visits increases as the number of months increases, the correlation is esolutions Manual - Powered by Cognero Page 3
4 positive 15 Write the piecewise function shown b Use the ordered pairs (1, 124) and (5, 192) Substitute m = 17 and (x, y) = (1, 124) in the slopeintercept form y = mx + b Substitute m = 17 and b = 107 in the slope-intercept form y = mx + b So, a prediction equation for the scatter plot is c Substitute x = 6 in the equation So, there will be 209 number of emergency room visits for March 14 Graph Graph the function f (x) 16 Identify the domain and range of The greatest integer function is defined for all real numbers So, the domain of the function is all real numbers The greatest integer function takes values from the set of all integers So, the range of the function is all integers 17 Describe the translation to y = x To obtain the graph of y = x 2 + 5, shift the graph of y = x 2 by 5 units upwards 18 Describe the reflection in To obtain the graph of over the x-axis, reflect the graph of esolutions Manual - Powered by Cognero Page 4
5 19 Graph each inequality 20 esolutions Manual - Powered by Cognero Page 5
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