University math

If Log_x (1 / 8) = - 3 / 2, then x is equal to

• A. - 4

• B. 4

• C. 1 / 4

• D. 10

20 % of 2 is equal to

• A. 20

• B. 4

• C. 0.4

• D. 0.04

If Log ₄ (x) = 12, then log ₂ (x / 4) is equal to

• A. 11

• B. 48

• C. -12 ANSWER

• D. 22

The population of a country increased by an average of 2% per year from 2000 to 2003. If the population of this country was 2 000 000 on December 31, 2003, then the population of this country on January 1, 2000, to the nearest thousand would have been

• A. 1 846 000

• B. 1 852 000

• C. 1 000 000

• D. 1 500 000

f is a quadratic function whose graph is a parabola opening upward and has a vertex on the x-axis. The graph of the new function g defined by g(x) = 2 - f(x - 5) has a range defined by the interval

• A. [ -5 , + infinity)

• B. [ 2 , + infinity)

• C. ( - infinity , 2]

• D. ( - infinity , 0]

f is a function such that f(x) < 0. The graph of the new function g defined by g(x) = | f(x) | is a reflection of the graph of f

• A. on the y axis

• B. on the x axis

• C. on the line y = x

• D. on the line y = - x

If the graph of y = f(x) is transformed into the graph of 2y - 6 = - 4 f(x - 3), point (a , b) on the graph of y = f(x) becomes point (A , B) on the graph of 2y - 6 = - 4 f(x - 3) where A and B are given by

• A. A = a - 3, B = b

• B. A = a - 3, B = b

• C. A = a + 3, B = -2 b

• D. A = a + 3, B = -2 b +3

When a parabola represented by the equation y - 2x ² = 8 x + 5 is translated 3 units to the left and 2 units up, the new parabola has its vertex at

• A. (-5 , -1)

• B. (-5 , -5)

• C. (-1 , -3)

• D. (-2 , -3)

The graphs of the two linear equations a x + b y = c and b x - a y = c, where a, b and c are all not equal to zero,

• A. are parallel

• B. intersect at one point

• C. intersect at two points

• D. perpendicular

The graphs of the two equations y = a x ² + b x + c and y = A x ² + B x + C, such that a and A have different signs and that the quantities b ² - 4 a c and B ² - 4 A C are both negative,

• A. intersect at two points

• B. intersect at one point

• C. do not intersect

• D. none of the above