Question 1

A biologist is tracking the movement of a tagged animal. On Monday, the animal is at $$(2, 3)$$, and on Friday, it is at $$(6, 11). $$What is the distance the animal traveled, assuming a straight path?

Accepted Answer

$$\sqrt{80}$$

Question 2

A medical researcher models the spread of a virus using $$f(x) = \sqrt{x - 5}. $$What is the domain of this function?

Accepted Answer

$$x \geq 5$$

Question 3

A city planner wants to find the midpoint between two locations: $$(-4, 5)$$ and $$(2, -1). $$What are the coordinates of the midpoint?

Accepted Answer

$$(-1, 2)$$

Question 4

A line passes through the point $$(1, 4)$$ and has a slope of $$3. $$Which of the following is the correct equation for this line?

Accepted Answer

$$y = 3x + 1$$

Question 5

Solve the absolute value equation $$|x - 3| = 7$$ for $$x. $$Which set contains all solutions?

Accepted Answer

$$\{10, -4\}$$

Question 6

A circular park has the equation $$(x - 2)^2$ + (y + 1)^2$ = 9. $$What is the center and radius of the park?

Accepted Answer

Center: $$(2, -1)$$, Radius: $$3$$

Question 7

A chemist measures the rate of change in concentration using $$f(x) = x^2$ from x = 1$ to x = 3$. What is the average rate of change?

Accepted Answer

$$4$$

Question 8

A line passes through $$(-2, 5)$$ and $$(4, -1). $$What is the slope of the line?

Accepted Answer

Question 9

A line is parallel to $$y = 2x - 3$$ and passes through $$(0, 5). $$What is its equation?

Accepted Answer

$$y = 2x + 5$$

Question 10

Solve $$2|x + 4| = 10$$ for $$x. $$Which set contains all solutions?

Accepted Answer

$$\{1, -9\}$$

Question 11

A student is asked to find the difference quotient for $$f(x) = x^2$ at x$ with increment h$. What is the simplified form?

Accepted Answer

$$2x + h$$

Question 12

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

Accepted Answer

$$2$$

Question 13

A rational function $$f(x) = \frac{1}{x - 2}$$ models a chemical reaction rate. What is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 2$$

Question 14

If $$|x - 5| \u003c 3$$, what is the solution set for $$x$$?

Accepted Answer

$$2 \u003c x \u003c 8$$

Question 15

A circle has equation $$(x + 3)^2$ + (y - 2)^2$ = 16. $$What is the radius?

Accepted Answer

$$4$$

Question 16

A line passes through $$(0, 0)$$ and $$(5, 10). $$What is its slope?

Accepted Answer

$$2$$

Question 17

A function $$f(x) = \sqrt{9 - x} is $$used to model a physical process. What is the domain of $$f(x)$$?

Accepted Answer

$$x \leq 9$$

Question 18

A line passes through $$(2, -3)$$ and is perpendicular to $$y = 4x + 1. $$What is the slope of the new line?

Accepted Answer

$$-\frac{1}{4}$$

Question 19

A business tracks profit using $$f(x) = 5x - 2. $$What is the average rate of change from $$x = 2 to$$ $$x = 6$$?

Accepted Answer

$$5$$

Question 20

A student solves the inequality $$-2x \u003e 6. $$What is the correct solution?

Accepted Answer

$$x \u003c -3$$

College Algebra: Core Concepts and Practice for Test 1

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드