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Your Pre-Calc Exam > Pre-Calc Exam 1 > Flashcards

Pre-Calc Exam 1 Flashcards

1
Q

Find y-intercept(s) and x-intercept(s) of y = 2(x^2) - x - 1

A

y-intercept: (0, -1) x-intercepts: (-1/2, 0) and (1, 0)

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2
Q

Find y-intercept(s) and x-intercept(s) of y = 3(x^2) - 12

A

y = 3(x^2) +0x - 12 y-intercept: (0, -12) x-intercepts: (2, 0) and (-2, 0)

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3
Q

Find y-intercept(s) and x-intercept(s) of y = x + 3

A

y-intercept: (0, 3) x-intercept: (-3, 0)

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4
Q

Find y-intercept(s) and x-intercept(s) of y = (x^2) + 6x + 9

A

y-intercept: (0, 9) x-intercept: (-3, 0)

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5
Q

Find y-intercept(s) and x-intercept(s) of y = 3(x^2) + 18x + 27

A

y-intercept: (0, 27) x-intercept: (-3, 0)

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6
Q

Find y-intercept(s) and x-intercept(s) of y = x^2 + 4x + 5

A

y-intercept: (0, 5) x-intercept: 0 = x^2 + 4x + 5 x = [-b +/- sqrt(b^2 -4ac)]/2a x = [-2 +/- sqrt(2^2 -4*1*5)]/(2*1) = [-2 +/- sqrt(4-20)]/2 therefore, x-int = undefined

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7
Q

Find the inverse function of f(x) = 2x + 3

A

f(x) = y = 2x+3 y -3 = 2x (y-3)/2 = x [f(x)-3]/2 = f’(x)

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8
Q

Find the inverse function of f(x) = x + 1

A

f(x) = y = x + 1 y = x + 1 y-1 = x f(x) - 1 = f’(x)

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9
Q

Find the inverse function of f(x) = 2(x^2) - x -1

A

f(x) = y = 2(x^2) - x -1 y = 2(x^2) - x - 1 y + 1 = 2(x^2) - x (y + 1)/2 = (x^2) - (x/2) + (1/4) (y+1)/2 + 1/4= (x+ 1/2)^2 sqrt[(y+1)/2 + 1/4] = sqrt[(x+ 1/2)^2] sqrt[(y+1)/2 + 1/4] = x+ 1/2 sqrt[(y+1)/2 + 1/4] - 1/2 = x sqrt{[f(x)+1]/2 + 1/4} - 1/2 = f’(x)

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10
Q

Find the inverse function of f(x) = x^2 + 6x + 9

A

f(x) = y = x^2 + 6x + 9 y = x^2 + 6x + 9 y = (x+3)^2 sqrt(y) = sqrt[(x+3)^2] sqrt(y) = x + 3 sqrt(y) - 3 = x sqrt[f(x)] - 3 = f’(x)

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11
Q

Find the inverse function of f(x) = x^2 -12x + 36

A

f(x) = y = x^2 -12x + 36 y = x^2 -12x + 36 y = (x-6)^2 sqrt(y) = sqrt[(x-6)^2] sqrt(y) = (x-6) sqrt(y) + 6 = x sqrt[f(x)] + 6 = f’(x)

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12
Q

Find the inverse function of f(x) = 3(x^2) + 5x + 25

A

f(x) = y = 3(x^2) + 5x + 25 y = 3(x^2) + 5x + 25 y - 25 = 3(x^2) + 5x (y - 25)/3 = [3(x^2) + 5x]/3 (y - 25)/3 = (x^2) + 5x/3 (y - 25)/3 + [(5/3)/2]^2 = (x^2) + 5x/3 + [(5/3)/2]^2 (y - 25)/3 + (5/6)^2 = (x^2) + 5x/3 + (5/6)^2 (y - 25)/3 + 25/36 = (x^2) + 5x/3 + 25/36 (y - 25)/3 + 25/36 = (x + 5/6)^2 sqrt[(y - 25)/3 + 25/36] = sqrt[(x + 5/6)^2] sqrt[(y - 25)/3 + 25/36] = x + 5/6 sqrt[(y - 25)/3 + 25/36] -5/6 = x sqrt{[f(x) - 25]/3 + 25/36} -5/6 = f’(x)

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13
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 1. The solution to the equation 3x − 2 = 4 is x = 7/2

A

False because the solution to the equation 3x − 2 = 4 is x = 2.

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14
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 2. The solutions to the equation x^2 − 3x + 2 = 0 are x = 2 and x = −1.

A

(x-1)(x-2)=0 x=1, 2 Therefore, false. The solutions to the equation x^2 − 3x + 2 = 0 are x=1 and 2.

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15
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 3. The zeros of f (x) = x^2 + 2x − 4 are irrational numbers.

A

f(x) = (x^2 +2x) -4 f(x) = (x^2 + 2x +1) - 4 + 1 f(x) = (x-1)^2 -3 (x-1)^2 - 3 = 0 (x-1)^2 = 3 sqrt[(x-1)^2] = sqrt(3) x-1 = sqrt(3) x = sqrt(3)+1 Therefore, true.

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16
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 4. The zeros of f(x) = 2(x^3) − x^2 − x are rational numbers.

A

Answer

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17
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 5. The solution set of the inequality 2x + 1

A

Answer

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18
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 6. The solution set of the inequality −3x + 4 ≥ 10 is the interval (−∞,−2].

A

Answer

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19
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 7. The only solution to |3x − 4| = 2 is x = 2/3.

A

Answer

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20
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 8. The solution set of the inequality |x − 4| ≤ 3 is the interval [1, 7].

A

Answer

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21
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 9. If |x − 5| = 3, then the distance from x to 5 is 3.

A

Answer

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22
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 10. If |2x − 5| = 3, then the distance from x to 52 is 32.

A

Answer

23
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 11. The domain of the function f (x) =sqrt(x − 3) is [−3,∞).

A

Answer

24
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 12. The domain of the function f (x)= xsqrt(x − 3) is [3,∞).

A

Answer

25
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 13. The domain of the function f(x)= sqrt[(x +1)(x −2)] is (−∞,−1] ∪ [2,∞).

A

Answer

26
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 14. The domain of the function f(x) = sqrt(x^2 + x − 2) is (−∞,−2] ∪ [1,∞).

A

Answer

27
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 15. The center of the circle (x − 2)^2 + y^2 = 4 is (2, 0) and the radius is 4.

A

Answer

28
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 16. The center of the circle x^2 + 2x + y^2 − 4y = 4 is (1, 2) and the radius is 3.

A

Answer

29
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 17. The slope of the line 2x − 3y = 4 is −23.

A

Answer

30
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 18. The lines x + y = 2 and 3x −2y = 1 intersect at the point (2, 1).

A

Answer

31
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 19. The lines −3x + 2y = 5 and 4y = 6x + 7 are perpendicular.

A

Answer

32
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 20. The lines x − 3y = 3 and 4x − 6y = 5 are parallel.

A

Answer

33
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 21. The lines 2x + y = 2 and 2y + x = −1 are perpendicular.

A

Answer

34
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 22. The lines x + 2y = 1 and −2x + y = 3 are parallel.

A

Answer

35
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 23. The equation of the line that has slope −3 and passes through the point (0, 1) is y = −3x − 1.

A

Answer

36
Q

Opposite of exponents/how do you undo an exponent

A

By taking the root of that power. For example, to undo a square, take the square root. To undo a cube, cube root it.

37
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 24. The equation of the line that passes through the two points (2, 1) and (−3, 2) is 5y − x = 7.

A

Answer

38
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true. 25. The shaded region is described by y ≤ 1.

A

Answer

39
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The region outside the shaded region is described by
    y > 1.
A

Answer

40
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The shaded region is described by 0 ≤ x < 2.
A

Answer

41
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The region outside the shaded region is described by
    x < 0 or x ≥ 2.
A

Answer

42
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The shaded region is described by |x − 1| ≤ 3 and
    |y + 1| < 2.
A

Answer

43
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The region outside the shaded region is described by
    |x − 1| > 3 and |y + 1| ≥ 2.
A

Answer

44
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The vertex of the parabola y = x2 + 4x + 3 is at (−2,−1).
A

Answer

45
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

32. The parabola y = −(x + 1)^2 − 2 has a maximum
point at (−1, 2).
A

Answer

46
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The domain of the function is (−∞,−1) ∪ (−1, 1) ∪ (1,∞).
A

Answer

47
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The range of the function is (−∞, 0] ∪ (2,∞).
A

Answer

48
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The difference quotient for the function f (x) = −2x + 3 reduces to −2.
A

Answer

49
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The difference quotient for the function f (x) = −2x + 3 reduces to −2.
A

Answer.

50
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make
it true.

  1. The difference quotient for the function
    f (x) = x^2 + 2x − 1 reduces to 2x + 2 + h.
A
51
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The graph of an even function is symmetric with
    respect to the origin and the graph of an odd function
    is symmetric with respect to the y-axis.
A

Answer

52
Q

Determine whether the statement is true or false. If false, describe how the statement might be changed to make it true.

  1. The graph of y = −f (x) is the reflection of the
    graph of y = f (x) about the y-axis.
A

Answer

53
Q

Find the solutions of x in

0 <= (4-x)sqrt(5-x)/{x sqrt[(x+4)(x-1)^1/3]}

AND write out the solutions of x as an inequality and as an interval notation.

A

Answer

54
Q

y=a[sin(b(x-h))]+k, where

k= center line,

a=height of both directions, and

h=shift to the right or left

Y=-0.5sin(2x-3.14/4)+2

Find: vertical shift, horizontal shift, amplitude, reflection, period, period 1 start, period 1 end, period 2 start and period 2 end, minimum, and maximum

A

Your Pre-Calc Exam (1 decks)

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