$$V(6) = 20000 - 1500 \times 6 = 11000$$

$$2 \times 16 - 3 \times 4 + 1 = 32 - 12 + 1 = 21$$

Question 1

Which of the following expressions is equivalent to $$(-3)^2 + 5(-3) + 8$?

Accepted Answer

$$9 - 15 + 8$$

Question 2

Given the function $$f(x) = \dfrac{x^2$ - 5x + 2}{x + 10}$$, what is $$f(-10)$$?

Accepted Answer

Undefined

Question 3

Which of the following is the correct interval notation for: 'Kayla got at least an 80 on the quiz, but no more than a 95'?

Accepted Answer

$$[80, 95]$$

Question 4

A company’s profit $$P (in $$dollars) from selling $$x$$ units is given by $$P(x) = 20x - 500. $$What does the number 20 represent in this context?

Accepted Answer

The profit per unit sold

Question 5

Given the linear function $$y = -3x + 7$$, what is the slope and what does it indicate about the function?

Accepted Answer

Slope is $$-3$$; the function is decreasing

Question 6

A car’s value $$V (in $$dollars) after $$t$$ years is modeled by $$V(t) = 20000 - 1500t. $$What is the value of the car after 6 years?

Accepted Answer

$$V(6) = 20000 - 1500 	imes 6 = 11000$$

Question 7

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

Accepted Answer

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

Question 8

A population grows from 50,000 to 80,000 over 10 years. What is the average rate of change per year?

Accepted Answer

$$3,000$$ people per year

Question 9

Which of the following is the correct slope-intercept form of the equation $$4x - 2y = 8$$?

Accepted Answer

$$y = 2x - 4$$

Question 10

A function $$f is $$defined as $$f(x) = 2x^2$ - 3x + 1. $$What is $$f(4)$$?

Accepted Answer

$$2 	imes 16 - 3 	imes 4 + 1 = 32 - 12 + 1 = 21$$

Question 11

Which of the following intervals represents all $$x$$ such that $$x \u003e 2$$ and $$x \leq 7$$?

Accepted Answer

$$(2, 7]$$

Question 12

If a function $$f is $$constant on the interval $$[1, 5]$$, which of the following statements is true?

Accepted Answer

$$f(x)$$ has the same value for all $$x in$$ $$[1, 5]$$

Question 13

A company’s cost to produce $$x$$ items is $$C(x) = 1200 + 15x. $$What is the fixed cost?

Accepted Answer

$$1200$$

Question 14

Given the points $$(2, 5)$$ and $$(6, 13)$$, what is the slope of the line passing through them?

Accepted Answer

$$\dfrac{13 - 5}{6 - 2} = 2$$

Question 15

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

Accepted Answer

$$[0, \infty)$$

Question 16

A linear function models the cost $$C (in $$dollars) to rent a car for $$d$$ days: $$C(d) = 40d + 25. $$What does the 25 represent?

Accepted Answer

The initial fixed cost (base fee)

Question 17

If the average rate of change of a function $$f$$ from $$x = 1 to$$ $$x = 4 is $$zero, what can you conclude about $$f on$$ $$[1, 4]$$?

Accepted Answer

$$f is $$constant on $$[1, 4]$$

Question 18

A student’s GPA $$G is $$more than 2.0 but at most 4.0. Which interval notation represents this?

Accepted Answer

$$(2.0, 4.0]$$

Question 19

A function $$f is $$increasing on the interval $$(-2, 5). $$Which of the following is true?

Accepted Answer

$$f(x)$$ increases as $$x$$ increases from $$-2 to$$ $$5$$

College Algebra Math 130A: Chapter 1 Study Notes

스터디 가이드 - 연습 문제