College Algebra. Chapter 1 Review Created by: Lauren Atkinson. Math Coordinator, Mary Stangler Center for Academic Success

Transcription

1 College Algebra Chapter 1 Review Created by: Lauren Atkinson Math Coordinator, Mary Stangler Center for Academic Success

2 Note: This review is composed of questions from the chapter review at the end of chapter 1. This review is meant to highlight basic concepts from chapter 1. It does not cover all concepts presented by your instructor. Refer back to your notes, unit objectives, handouts, etc. to further prepare for your exam.

3 Classify each number listed as one or more of the following: natural number, integer, rational number, or real number. 55,1.5, , 23, 3, 1000 Natural numbers: 1,2,3,4, Integer:, 3, 2, 1,0,1,2,3, Rational numbers: can be written as p where p and q are integers; includes q repeating and terminating decimals. Real numbers: any number that can be expressed in decimal form; includes rational and irrational numbers. 55 = natural, integer, rational, real 1.5 = rational, real = rational, real 2 3 = natural, integer, rational, real 3 = real 1000 = integer, rational, real

4 Write the number in scientific notation: We have moved the decimal point 4 spots to the right so our scientific notation becomes the following:

5 Write the number in standard form: We have moved the decimal point 3 spots to the left so our standard form becomes the following:.0072

6 Evaluate each expression. Write your answer in scientific notation and in standard form. a) = = 0.2, b) = = ,

7 Evaluate by hand: = = = 108

8 Determine the minimum and maximum values of the set of data. Calculate the mean and median. 8.9, 1.2, 3.8,0.8,1.7,1.7 Arrange data from smallest to largest: 3.8, 1.2, 0.8, 1.7, 1.7, 8. 9 Maximum: 8.9 Minimum: -3.8 Mean: Median: = = 1.35

9 Express the data as a relation S. Find the domain and range of S. X Y S = 0.6,10, 0.2,20, 0.1,25, 0.5,30, (1.2,80) domain refers to all of the x-coordinates, range refers to all of the y-coordinates. DOMAIN always refers to x, RANGE always refers to y. domain = 0.6, 0.2,0.1,0.5,1.2 range = {10,20,25,30,80}

10 Determine if the relation is a function: YES { 1.5,2.5, 0,2.1, 2.3,3.1, 0.5, 0.8, 1.1,0 } A relation is a function if for every input of x, there is exactly only one output for y. To illustrate this: Since each input (green circle) value corresponds to only one output (blue circle), the relation is a function.

11 Find the distance between the two points: 1.2, 4, (0.2,6) d = (x 2 x 1 ) 2 +(y 2 y 1 ) 2 d = ( ) 2 +(6 4 ) 2 d = 101

12 Find the midpoint of the line segment with the given endpoints. 1, 5, 1, Midpoint = x 1+x 2 2 = , = 1 2, 5 8, y 1+y 2 2

13 Find the standard equation of a circle with center (-5,3) and radius 9. The circle with center (h,k) and radius r has the equation: (x h) 2 +(y k) 2 = r 2 = (x + 5) 2 +(y 3) 2 = 81

14 Graph y = f(x) by first plotting points to determine the shape of the graph. f x = 3x f x = 2x 3 f x = 1 2 x2 1 f x = 3 x

15 Evaluate f(x) at the indicated values of x. Find the domain of f. f x = 4 5x for x = 5,6 f 5 = = = 29 f 6 = = 4 30 = 26 domain = all real numbers f x = x 3 3x for x = 10, a + 1 f 10 = = 970 f a + 1 = a a + 1 = a 3 + 3a 2 2 domain = all real numbers

16 Evaluate f(x) at the indicated values of x. Find the domain of f. f x = x + 3 for x = 1, a 3 f 1 = = 4 = 2 f a 3 = a = a domain = all real numbers greater than or equal to 3

17 Write 5 x < 10 in interval notation. [5,10) Determine if S represents a function: S = 1,3, 0,2, 1,7, 3, 3 This is similar to the table/relation question from before. Does every output of x only have one output of y? NO, since -1 (input) corresponds to both 3 and 7, this is not a function.

18 State the slope of the graph f: f x = 1 3 x 2 3 Slope is always the m in f x so in our equation, the m = 1 3. = mx + b;

19 Find the slope of the line passing through each pair of points. 1, 4, (2,10) m = y 2 y 1 = 10 ( 4) x 2 x = 14 1 = 14 1, 2, 1, m = = = undefined

20 Decide whether the function f is constant, linear or nonlinear. f x = 2x 2 3x 8 NONLINEAR, because the highest power on the x variable is not 1. This function has a power of 2 on x. f x = 6 CONSTANT (and linear), because there is not an x variable in the equation. f x = 3x + 24 LINEAR, because the highest power on the variable is 1.

21 Determine where the graph of f x = x 3 is increasing and where it is decreasing. Graph this function first: From the graph, we can see where it is increasing (positive slope) and where it is decreasing (negative slope): Increasing: 3, Decreasing: (, 3]

22 Find the average rate of change of f x = x 2 x + 1 from x 1 = 1 to x 2 = 3. Average rate of change, means to find the slope: f 1 = (1) = 1 f 3 = (3) = 7 Giving two ordered pairs: 1,1, 3,7 Then compute the slope: = 6 2 = 3 Average rate of change is 3.

23 The rest of the chapter review covers the application problems. There will be application problems on the exam so study accordingly.