Q: A chemist is mixing two solutions: Solution A contains 30% acid and Solution B contains 50% acid. How many liters of each solution should be mixed to obtain 10 liters of a solution that is 40% acid? Let $$x be $$the liters of Solution A used. Which equation correctly models this scenario?

$$0.3x + 0.5(10 - x) = 0.4 \times 10$$

Question 1

A chemist is mixing two solutions: Solution A contains 30% acid and Solution B contains 50% acid. How many liters of each solution should be mixed to obtain 10 liters of a solution that is 40% acid? Let $$x be $$the liters of Solution A used. Which equation correctly models this scenario?

Accepted Answer

$$0.3x + 0.5(10 - x) = 0.4 	imes 10$$

Question 2

Which of the following equations does NOT represent a function?

Accepted Answer

$$x = y^2$

Question 3

Given the function $$f(x) = x^3$ - 2x$$, determine if $$f(x) is $$even, odd, or neither.

Accepted Answer

Odd

Question 4

A company’s profit $$P (in $$thousands of dollars) after selling $$x$$ units is modeled by $$P(x) = 5x - 200. $$What does the $$y-$$intercept represent in this context?

Accepted Answer

The profit when no units are sold, which is a loss of $200,000

Question 5

Given the function $$f(x) = |x - 2|$$, what is the domain and range of $$f(x)$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[0, \infty)$$

Question 6

Which of the following intervals describes where the function $$f(x) = -x^2$ + 4 is $$increasing?

Accepted Answer

$$(-\infty, 0)$$

Question 7

Given the points $$(2, 5)$$ and $$(6, 13)$$, what is the equation of the line passing through these points in slope-intercept form?

Accepted Answer

$$y = 2x + 1$$

Question 8

A line passes through the point $$(3, -2)$$ and is perpendicular to the line $$y = -\frac{1}{2}x + 4. $$What is the equation of the new line?

Accepted Answer

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

Question 9

Evaluate $$f(-3)$$ for the piecewise function:

$$ f(x) = \begin{cases} x^2$ + 1 & x \u003c 0 \ 2x - 1 & x \geq 0 \end{cases} $$

Accepted Answer

$$10$$

Question 10

Find the difference quotient for $$f(x) = x^2$ + 2x.$$

Accepted Answer

$$2x + h + 2$$

Question 11

Which of the following best describes the range of the function $$f(x) = \sqrt{x - 3}$$?

Accepted Answer

$$[0, \infty)$$

Question 12

A taxi company charges a flat fee of $$\4$ plus $$\$$2$$ per mile. Which function models the total cost $$C$$ for $$x$$ miles?

Accepted Answer

$$C(x) = 2x + 4$$

Question 13

Given the function $$f(x) = x^2$ - 4x + 3$$, at what $$x-$$value does the function attain its minimum value?

Accepted Answer

$$x = 2$$

Question 14

Which of the following is the $$x-$$intercept of the line $$y = 3x - 6$$?

Accepted Answer

$$(2, 0)$$

Question 15

Suppose $$f(x) is $$defined as $$f(x) = \begin{cases} 2x + 1 & x \u003c 1 \ x^2$ & x \geq 1 \end{cases}. $$What is $$f(1)$$?

Accepted Answer

$$1$$

Question 16

Which of the following is the correct set-builder notation for the domain of $$f(x) = \frac{1}{x - 5}$$?

Accepted Answer

$$\{ x \mid x 
eq 5 \}$$

Question 17

A biologist models the population of a bacteria culture by $$P(t) = 1000 + 200t$$, where $$t is $$time in hours. What does the slope represent in this context?

Accepted Answer

The population increases by 200 bacteria per hour

Question 18

Given the function $$f(x) = 3x - 7$$, evaluate $$f(4).$$

Accepted Answer

$$5$$

Question 19

Which of the following describes where the function $$f(x) = x^3$ is decreasing?

Accepted Answer

Nowhere; $$f(x) is $$always increasing or decreasing depending on the sign of $$x$$

Question 20

Which of the following is the correct interval notation for the range of $$f(x) = 2x + 5$$?

Accepted Answer

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

College Algebra Study Guide: Functions and Linear Models

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