Question 1

Which of the following relations is NOT a function?

Accepted Answer

The relation $$x = y^2$

Question 2

Given the function $$f(x) = 3x - 5$$, what is the value of $$f^{-1}(7$$)$$?

Accepted Answer

$$4$$

Question 3

A company’s revenue $$R (in $$dollars) from selling $$x$$ units of a product is modeled by $$R(x) = 50x - 0.5x^2$. What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $$1250 at$$ $$x = 50$$

Question 4

Which of the following describes the transformation of the graph of $$f(x) = x^2$ to g(x$$) = $$-2(x-3)^2 + 4$?

Accepted Answer

Shift right 3 units, stretch vertically by 2, reflect over $$x-$$axis, shift up 4 units

Question 5

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$19$$

Question 6

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

Accepted Answer

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

Question 7

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 3$$^{t/4}$$

Question 8

Solve the equation $$2^{x+1} = 16$ for x$.

Accepted Answer

$$3$$

Question 9

Which of the following is the inverse of the function $$f(x) = \ln(x-2)$$?

Accepted Answer

$$f^{-1}(x) = e^x + 2$

Question 10

A medical test result is modeled by the function $$T(x) = 5 \log_{10}(x) + 7$$, where $$x is $$the concentration of a substance. If the test result is $$T = 12$$, what is the concentration $$x$$?

Accepted Answer

$$x = 100$$

Question 11

Which of the following statements is TRUE about the function $$f(x) = x^3$?

Accepted Answer

$$f(x) is an $$odd function

Question 12

Given the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$, what is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1)$$

Question 13

A piecewise function is defined as $$f(x) = \begin{cases} x+2 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}. $$What is $$f(-3) + f(2)$$?

Accepted Answer

$$7$$

Question 14

Which of the following best describes the range of the function $$f(x) = \dfrac{2x}{x^2$ + 1}$$?

Accepted Answer

$$(-1, 1)$$ including 0$

Question 15

A car depreciates in value according to the function $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value of the car after 3 years?

Accepted Answer

$$12206.25$$

Question 16

Which of the following is the solution set to the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$(2, 3)$$

Question 17

If $$f(x) = 4x - 7$$ and $$g(x) = x^2$, what is (f + g)(-2$$)$$?

Accepted Answer

$$1$$

Question 18

A chemist mixes two solutions: one with 30% acid and one with 10% acid. How many liters of each should be mixed to obtain 20 liters of a 25% acid solution?

Accepted Answer

$$15$$ liters of 30% and $$5$$ liters of 10% solution

Question 19

Which of the following is the correct equation of the line passing through the points $$(1, 2)$$ and $$(3, 6)$$?

Accepted Answer

$$y = 2x$$

Question 20

If $$f(x) = \log_2$(x)$$, what is the value of $$f(8) + f(0.5)$$?

Accepted Answer

$$2$$

Math 1111: College Algebra Course Description, Goals, and Student Learning Outcomes

Guida di studio - Domande di pratica

Study guide - Flashcard