Quadratic Inequality

15. (1 mark) The y-intercept of the function y = 7x + 1 is .

A. y = 1

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B. y = 2

C. y = 7

D. y = 1

7

16. (1 mark) What is the solution to the quadratic inequality (1 −x)(1 + x) ≤ 0?

A. x ≥−1 and x ≤ 1

B. x ≤ 1 or x ≤−1

C. x ≤−1 or x ≥ 1

D. x ≥−1 or x ≤ 1

17. (1 mark) What is the horizontal asymptote of the rational function r(x) = 2×2 − 5x + 2 3×2 + x + 4

?

A. y = 3

2

B. y = 2

3

C. x = 2

3

D. x = 3

2

18. (1 mark) Which of the following rational function does not have a vertical asymp- tote?

A. 1

x− 1

B. 1

x + 1

C. 1

x2 − 1

D. 1

x2 + 1

19. (1 mark) After a parent function f(x) = 5x has been stretched horizontally by a factor of 2, and then shifted 7 units down, what is the new equation?

A. g(x) = 5 x 2 − 7

B. g(x) = 52x − 7

C. g(x) = 5( x 2 −7)

 

D. g(x) = 5(2x−7)

20. (1 mark) Within the interval 0 ≤ x ≤ 2π, the graph of sin(x) crosses the x-axis at three points: x = 0,π, 2π. After a transformation of the form sin(kx), with k > 1, how are the x-intercepts affected within the same interval?

A. the new graph has three x-intercepts as before.

B. the new graph has more than three x-intercepts.

C. the new graph as less than three x-intercepts.

D. the new graph does not have any x-intercepts.

21. (1 mark) A solution to the trigonometric equation cos(x) = − 1

2 is .

A. x = π

3

B. x = π

6

C. x = 2π

3

D. x = π

2

22. (1 mark) The equation sin(x) = csc(x)

A. is an identity.

B. has no solution.

C. has two solutions within the interval 0 ≤ x ≤ π.

D. has two solutions within the interval 0 ≤ x ≤ 2π.

23. (1 mark) The double-angle expansion for cos(2x) is .

A. cos2(x) − 2 sin(x)

B. cos2(x) − sin2(x)

C. sin2(x) − cos2(x)

D. sin2(x) − 2 cos(x)

24. (1 mark) What is the maximum value of f(x) = 2 sin[3(x + π)] − 8?

A. -10

B. -6

C. 6

D. 10

 

25. (1 mark) If cot(x) = − 3

4 and x is in quadrant II, then

A. sin(x) = − 3

5

B. cos(x) = − 4

5

C. sin(x) = 4

5

D. cos(x) = 4

5

 

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