Question 1

Which of the following is the simplified form of $$ (2 + i)(3 - 2i) $$?

Accepted Answer

$$ 8 - i $$

Question 2

A medical imaging device uses the function $$ y = \sqrt{2x + 1}  to $$model the minimum detectable signal, where $$ x  is $$the exposure time in seconds. What is the domain of this function?

Accepted Answer

$$ [ -\frac{1}{2}, \infty ) $$

Question 3

A projectile is launched and its height in meters after $$ t $$ seconds is given by $$ h(t) = -4t^2$ + 8t + 2 . At $$what time(s) does the projectile reach a height of 10 meters?

Accepted Answer

$$ t = 1 + \sqrt{2} $$ and $$ t = 1 - \sqrt{2}  ($$only $$ t \u003e 0  is $$valid)

Question 4

Which of the following is the correct solution set for the inequality $$ x^2$ - x - 12 \u003c 0 $$?

Accepted Answer

$$ ( -3, 4 ) $$

Question 5

A circle has the equation $$ (x + 3)^2$ + (y - 4)^2$ = 36 . $$What are its center and radius?

Accepted Answer

Center $$ ( -3, 4 ) $$, radius $$ 6 $$

Question 6

A biologist is studying the population growth of bacteria, modeled by $$ P(t) = 500 \cdot 2$$^{t}$$ $$, where $$ t  is in $$hours. After how many hours will the population reach 4000?

Accepted Answer

$$ t = 4 $$

Question 7

Which of the following is the correct expansion of $$ y = \log_b \frac{mnq}{p^2$ t^4$} $$ using properties of logarithms?

Accepted Answer

$$ y = \log_b m + \log_b n + \log_b q - 2\log_b p - 4\log_b t $$

Question 8

A chemical reaction's rate is modeled by $$ y = 2x^2$ + 5x - 3 . $$What is the domain of this function?

Accepted Answer

$$ ( -\infty, \infty ) $$

Question 9

Which of the following is the correct solution to $$ \log_6$ (2x + 4) = 2 $$?

Accepted Answer

$$ x = 16 $$

Question 10

A line passes through the points $$ (2, 7) $$ and $$ (2, -4) . $$What is the slope of this line?

Accepted Answer

Undefined

Question 11

A parabola has the equation $$ y = x^2$ - 2x + 3 . $$What is its vertex?

Accepted Answer

$$ (1, 2) $$

Question 12

A patient’s medication level is modeled by $$ y = 2x^3$ + 5 $$, where $$ x  is $$time in hours. What is the inverse function $$ x  in $$terms of $$ y $$?

Accepted Answer

$$ x = \sqrt[3]{\frac{y - 5}{2}} $$

Question 13

Which of the following is the correct solution to the equation $$ 4x - 1 = 32x $$?

Accepted Answer

$$ x = -1.71 $$

Question 14

A circle is tangent to the x-axis and has center at $$ (3, 2) . $$What is its equation in center-radius form?

Accepted Answer

$$ (x - 3)^2$ + (y - 2)^2$ = 4 $$

Question 15

A line is perpendicular to $$ 3x + 5y = 1 $$ and passes through $$ (1, 6) . $$What is its equation in slope-intercept form?

Accepted Answer

$$ y = \frac{5}{3}x + \frac{13}{3} $$

Question 16

A quadratic equation $$ x^2$ + x + 1 = 0 $$ has which of the following solutions?

Accepted Answer

$$ x = \frac{ -1 \pm \sqrt{3}i }{2} $$

Question 17

A rational function $$ y = \frac{6}{(x-2)(x+3)} $$ has which domain?

Accepted Answer

$$ ( -\infty, -3 ) \cup ( -3, 2 ) \cup ( 2, \infty ) $$

Question 18

A patient’s heart rate is modeled by $$ y = 2x - 5 . If $$the heart rate is 3, what is the value of $$ x $$?

Accepted Answer

$$ x = 4 $$

Question 19

Which of the following is the correct solution to $$ |2x + 1| \u003c 7 $$?

Accepted Answer

$$ ( -4, 3 ) $$

Question 20

A parabola has the equation $$ y = 2x^2$ - 4x + 5 . $$What is its vertex?

Accepted Answer

$$ (1, 3) $$

Comprehensive Step-by-Step Guidance for College Algebra Final Exam Review

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