Precalculus FINAL REVIEW

Flashcards for vocabulary review of precalculus concepts.

The rectangular form of (-3 + 6i)(4 + 4i) is

-36 + 12i

The rectangular form of (-2 + 2i)(-3√2/2 - 3√2/2 i) is

6√2

The simplified form of (-4 + 2i) / (1 + 2i) is

2i

The simplified form of (-3 - 3i) / (5√2/2 - 5/2 i) is

(6√3 - 6) / 20 + (-6√3 - 6) / 20 i

End Behavior of f (x) = x^4 - 6x^3 + 11x^2 - 8x + 4

lim x→-∞ f (x) = ∞ and lim x→∞ f (x) = ∞

End Behavior of f (x) = x^4 - 4x^2 + x + 3

lim x→-∞ f (x) = ∞ and lim x→∞ f (x) = ∞

Zeros and End Behavior of f(x) = 2x^2 + 5x

Real zeros: {0, -5/2}; End behavior: lim x→-∞ f(x) = ∞, lim x→∞ f(x) = ∞

Zeros and End Behavior of f(x) = x^3 + 3x^2 + 3x + 1

Real zeros: {-1 mult. 3}; End behavior: lim x→-∞ f(x) = -∞, lim x→∞ f(x) = ∞

Rational Zeros and Zeros of f(x) = x^3 + 5x^2 - 4x - 20

Possible rational zeros: ±1, ±2, ±4, ±5, ±10, ±20; Zeros: {-5, 2, -2}

Rational Zeros and Zeros of f(x) = x^4 - 9

Possible rational zeros: ±1, ±3, ±9; Zeros: {√3, -√3, i√3, -i√3}

Is d(x) = 6x - 5 a factor of f(x) = 12x^2 - 22x - 2?

No, d(x) is not a factor of f(x)

Is d(x) = x + 1 a factor of f(x) = 11x^4 - 13x^2 + 4x + 6?

Yes, d(x) is a factor of f(x)

Roots of x^3 - 5x^2 - 4x + 20 = 0

{5, 2, -2}

Roots of x^5 + 6x^3 - 7x = 0

{0, i√7, -i√7, 1, -1}

Inverse of y = -4log_2(3x)

y = 2^(-x/4) / 3

Inverse of y = 2x - 5

y = (x + 5) / 2

Expanded Logarithm of log_7((u^5 / v)^6)

30log7(u) - 6log7(v)

Expanded Logarithm of log_7(11^4 * √(2 * 3))

4log7(11) + log7(2) + log_7(3)

Condensed Logarithm of 2ln(12) - 6ln(7)

ln(12^2 / 7^6)

Condensed Logarithm of log8(11) + log8(10^(1/3)) + log_8(7^(1/3))

log_8((11 * ∛70))

Solve 10^(k+6) + 5 = 1005

log(98) - 6

Solve 10 * 14^(3x - 5) + 6 = 52

(log_14(23/5) + 5) / 3

Solve ln(2x^2) - ln(8) = 2

{2e, -2e}

Solve log(x) - log(x + 5) = 1

No Solution

Transformation of f(x) = √x (reflect y-axis, compress vertically by 3, reflect x-axis, right 3, up 3)

g(x) = -1/3 * √(-(x - 3)) + 3

Transformation of f(x) = 1/x (expand vertically by 2, reflect x-axis, left 3, up 1)

g(x) = -2/(x + 3) + 1

Intercepts and Asymptotes of f(x) = 3 / (x - 2)

HA: y = 0, VA: x = 2; x-intercepts: None, y-intercept: -3/2

Intercepts and Asymptotes of f(x) = (x^2 - 3x) / (4x - 8)

HA: none, VA: x = 2; x-intercepts: 0, 3; y-intercept: 0

Initial Investment at 8% Continuous Interest to reach $11,268.48 after 15 years

$3,394

Time to reach $3,148.71 with $1,379 at 7% compounded twice per year

12 years

A bacteria population can grow indefinitely without limit. (TRUE or FALSE)

FALSE

The function f(x) = (x - 2) / 3 is even. (TRUE or FALSE)

TRUE

The logistic function has two horizontal asymptotes. (TRUE or FALSE)

TRUE

What is the y-intercept of the graph of f(x) = 2(x - 1)^3 + 5?

3

Rational function with vertical asymptote at x = -2 and removable discontinuity (hole) at x = 3

f(x) = ((x - 2)(x - 3)) / ((x + 2)(x - 3))

Rational function with a horizontal asymptote at y = 2

f(x) = 2 + 1 / (x^2 + 4)

If f(x) = √x and g(x) = x^(3/2), then (fg)(x) is equal to?

x^2

Solving log4(2x) + log4(x) = 4 gives x = ±√8

only √8 is a solution

lim x→-2 (-x + 2) / (x^2 + 6x + 8)

-1/2

lim x→-2 3 / (2x + 2)

-3/2

lim x→0 (x + 2) / (x^2 + 2x + 2)

1

lim x→-4 (-2x + 1)

3

lim x→2+ (x - 3) / (x^2 - 5x + 6)

∞

The rectangular form of (5 + 2i)(1 - 3i) is

11 - 13i

The rectangular form of (4 - i)(2√2/2 + 2√2/2 i) is

9√2 + 6√2i

The simplified form of (1 + 3i) / (2 - i) is

-1/5 + i7/5

The simplified form of (2 + 2i) / (2√2/2 + 3/2 i) is

(20√2 + 12)/41 + (20√2 - 12)/41 i

End Behavior of f(x) = -x^3 + 2x^2 - x + 5

lim x→-∞ f(x) = ∞ and lim x→∞ f(x) = -∞

End Behavior of f(x) = -2x^5 + 3x^2 - 1

lim x→-∞ f(x) = ∞ and lim x→∞ f(x) = -∞

Zeros and End Behavior of f(x) = -3x^2 + 7x

Real zeros: {0, 7/3}; End behavior: lim x→-∞ f(x) = -∞, lim x→∞ f(x) = -∞

Zeros and End Behavior of f(x) = x^3 - 5x^2 + 6x

Real zeros: {0, 2, 3}; End behavior: lim x→-∞ f(x) = -∞, lim x→∞ f(x) = ∞

Rational Zeros and Zeros of f(x) = x^3 - 3x^2 - x + 3

Possible rational zeros: ±1, ±3; Zeros: {-1, 1, 3}

Rational Zeros and Zeros of f(x) = x^4 - 16

Possible rational zeros: ±1, ±2, ±4, ±8, ±16; Zeros: {2, -2, 2i, -2i}

Is d(x) = 2x - 3 a factor of f(x) = 4x^2 + 4x - 3?

Yes, d(x) is a factor of f(x)

Is d(x) = x - 2 a factor of f(x) = 3x^3 - 5x^2 - 2x?

Yes, d(x) is a factor of f(x)

Roots of x^3 - 7x^2 + 10x = 0

{0, 2, 5}

Roots of x^5 + 8x^3 - 9x = 0

{0, i, -i, 1, -1}

Inverse of y = 5log₂(x/2)

y = 2^(x/5) * 2

Inverse of y = 3x + 7

y = (x - 7) / 3

Expanded Logarithm of log₃((a^7 / b)^4)

28log₃(a) - 4log₃(b)

Expanded Logarithm of log₅(3^2 * √(7 * 2))

2log₅(3) + log₅(7)/2 + log₅(2)/2

Condensed Logarithm of 3ln(5) - 7ln(3)

ln(5^3 / 3^7)

Condensed Logarithm of log₉(2) + log₉(5^(1/2)) + log₉(3^(1/2))

log₉((2 * √(15)))

Solve 5^(k+2) + 3 = 628

log₅(625) - 2 = 2

Solve 5 * 12^(2x - 4) + 2 = 27

(log₁₂(5) + 4) / 2

Solve ln(3x^2) - ln(6) = 3

{√(2e³), -√(2e³)}

Solve log(x) - log(x - 3) = 1

-10/3

Transformation of f(x) = √x (reflect x-axis, expand vertically by 4, left 1, down 2)

g(x) = -4 * √(x + 1) - 2

Transformation of f(x) = 1/x (compress vertically by 3, reflect y-axis, right 2, up 4)

g(x) = 1/3 * (1/(-x + 2)) + 4

Intercepts and Asymptotes of f(x) = 5 / (x + 1)

HA: y = 0, VA: x = -1; x-intercepts: None, y-intercept: 5

Intercepts and Asymptotes of f(x) = (x^2 - 4x) / (2x - 6)

HA: none, VA: x = 3; x-intercepts: 0, 4; y-intercept: 0

Initial Investment at 6% Continuous Interest to reach $15,000 after 10 years

$8,232.67

Time to reach $5,000 with $2,000 at 9% compounded monthly

10.23 years

The range of logistic functions will never include zero. (TRUE or FALSE)

TRUE

The function f(x) = (x + 3) / 5 is odd. (TRUE or FALSE)

FALSE

Exponential functions never have horizontal asymptotes. (TRUE or FALSE)

FALSE

What is the y-intercept of the graph of f(x) = -3(x + 2)^3 - 1?

-25

Rational function with vertical asymptote at x = 4 and removable discontinuity (hole) at x = -1

f(x) = ((x - 5)(x + 1)) / ((x - 4)(x + 1))

Rational function with a horizontal asymptote at y = -3

f(x) = -3 + 1 / (x^2 + 1)

If f(x) = √x and g(x) = x^(5/2), then (fg)(x) is equal to?

x^3

Solving log₂(x) + log₂(x) = 5 gives x = ±4

only 4 is a solution

lim x→3 (-x + 4) / (x^2 + 5x + 6)

1/149

lim x→-1 5 / (4x + 4)

does not exist

lim x→1 (x + 3) / (x^2 + 4x + 5)

1/5/4

lim x→-3 (-4x - 5)

7

lim x→4+ (x - 5) / (x^2 - 7x + 12)

-∞