Question 1

Which of the following is the simplified form of the expression $$\frac{(4xy$$^{-1}$$)^{\frac{3}$${2}}}{2xy}$, assuming all variables represent positive real numbers?

Accepted Answer

$$4x^{\frac{1}$${2}}$$y^{\frac{5}$${2}}$$

Question 2

What is the domain of the function $$f(x) = \frac{\sqrt{x-5}}{4}$$?

Accepted Answer

$$[5, \infty)$$

Question 3

Convert $$50^\circ to $$radians.

Accepted Answer

$$\frac{5\pi}{18}$$

Question 4

Which of the following functions represents a reflection of $$y = \sqrt{x}$$ across the $$x-$$axis?

Accepted Answer

$$-\sqrt{x}$$

Question 5

Find the intersection of the intervals $$(-4, 8] \cap (-\infty, 8).$$

Accepted Answer

$$(-4, 8)$$

Question 6

Which of the following is a factorization of the expression $$9x^6$$ - $$y^2$$?

Accepted Answer

$$(3x^3$$ - $$y)(3x^3 + y$$)$$

Question 7

Solve the equation $$2x^2 + 4x - 1 = 0$ for x$.

Accepted Answer

$$x = -2 \pm \frac{\sqrt{6}}{2}$$

Question 8

Which of the following is the equation of a line that is perpendicular to the line $$3x + 6y = 0$$?

Accepted Answer

$$y + 5 = 2(x - 3)$$

Question 9

Evaluate $$	an\left(\frac{5\pi}{6}ight).$$

Accepted Answer

$$-\frac{1}{\sqrt{3}}$$

Question 10

Determine the amplitude and period of the graph $$y = 3\sin\left(\frac{2\pi}{\pi}x\right).$$

Accepted Answer

amplitude = 3; period = $$\pi$$

Question 11

Solve the equation $$x = \frac{y + 2}{y - 1}$$ for $$y.$$

Accepted Answer

$$y = \frac{x + 1}{x - 2}$$

Question 12

Determine whether the function $$g(x) = \sin(x) + 4x^6$ is even, odd, or neither.

Accepted Answer

The function $$g is $$neither odd nor even.

Question 13

Assume all variables represent positive real numbers. Which of the following equalities is true?

Accepted Answer

$$\frac{2xy + x^2$z}{yz} = \frac{2x}{z} + \frac{x^2$}{y}$$

Question 14

A pharmaceutical company models the concentration of a drug in the bloodstream by $$C(t) = 5e$$^{-0.2t}$$, where t$ is time in hours. What is the concentration after 3 hours?

Accepted Answer

$$5e^{-0.6}$$

Question 15

A population of bacteria doubles every 4 hours. If the initial population is 500, what will the population be after 12 hours?

Accepted Answer

$$500 	imes 2^3$ = 4000$$

Question 16

A projectile is launched from ground level with a height function $$h(t) = -16t^2$ + 64t. At $$what time does it reach its maximum height?

Accepted Answer

$$t = 2$$

Question 17

Which of the following describes the transformation $$y = -2(x - 3)^2$ + 5$$ compared to $$y = x^2$?

Accepted Answer

Vertical stretch by 2, reflection across $$x-$$axis, right 3 units, up 5 units

Question 18

A chemical reaction is modeled by $$y = 100e$$^{-0.5t}$$, where y$ is the amount of reactant and t$ is time in hours. How long will it take for the reactant to decrease to 25 units?

Accepted Answer

$$t = 2.77$$

Question 19

A medical dosage is given by $$D(x) = \frac{10}{x}$$, where $$x is $$the number of hours since administration. What is the dosage after 5 hours?

Accepted Answer

$$2$$

Precalculus Exam 1: Step-by-Step Study Guidance

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