Question 1

A chemical reaction's temperature $$T (in $$degrees Celsius) is modeled by the function $$T(t) = 5t^2$ - 20t + 30$$, where $$t is $$the time in hours. What is the minimum temperature reached during the reaction, and at what time does it occur?

Accepted Answer

$$T = 10 at$$ $$t = 2$$

Question 2

Which of the following relations is a function?

Accepted Answer

$$\{ (1,2), (2,3), (3,4) \}$$

Question 3

Solve the quadratic equation $$x^2 - 6x + 5 = 0$ and select the correct solution set.

Accepted Answer

$$\{1, 5\}$$

Question 4

A biologist models the population of a bacteria culture by $$P(t) = 200 \cdot 2^t$$, where $$t is $$the number of hours since the start of the experiment. What is the population after 3 hours?

Accepted Answer

$$1600$$

Question 5

Which of the following equations represents a line perpendicular to $$y = -\frac{1}{2}x + 3$$?

Accepted Answer

$$y = 2x - 1$$

Question 6

Solve the absolute value equation $$|2x - 5| = 7.$$

Accepted Answer

$$x = 6,\ x = -1$$

Question 7

A company’s profit $$P (in $$thousands of dollars) is given by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

$$P = 18 at$$ $$x = 2$$

Question 8

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 9

Given the function $$f(x) = x^2$ - 3x + 2$$, what is $$f(4)$$?

Accepted Answer

$$6$$

Question 10

A medication’s concentration in the bloodstream is modeled by $$C(t) = 50e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 5 hours? (Round to the nearest whole number.)

Accepted Answer

$$18$$

Question 11

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$ + 1$$

Question 12

Solve the inequality $$2x - 3 \u003c 7$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 5)$$

Question 13

A car rental company charges a flat fee of $$\20$ plus $$\$$0.15$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles driven?

Accepted Answer

$$C = 0.15m + 20$$

Question 14

Which of the following intervals represents the range of the function $$f(x) = |x - 2|$$?

Accepted Answer

$$[0, \infty)$$

Question 15

If $$f(x) = 3x - 4$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$8$$

Question 16

A ball is thrown upward from a height of $$2$$ meters with an initial velocity of $$8 m/s. $$Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 8t + 2. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 0.82$$

Question 17

Which of the following best describes the symmetry of the function $$f(x) = x^4$ - 2x^2$?

Accepted Answer

Even; symmetric with respect to the $$y-$$axis

Question 18

Solve the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 3$$

Question 19

Which of the following is the solution set for the inequality $$|x + 4| \leq 2$$?

Accepted Answer

$$[-6, -2]$$

College Algebra Exam 1 Review: Comprehensive Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard