LUOA algebra 2: module 2 week 1

a compound statement that uses the word 'or' is called a....

disjunction

The equation of a line of best fit relating the money earned e at a bake sale to the number of customers c is e = 1.1c + 19. Use the equation to predict the earnings from a bake sale with 80 customers.

$107

a _________ ___________ is made up of one or more statement or inequality.

compound statement

Identify the solution of the compound inequality x + 4 > 9 or 2x ≥ 14 and the graph that represents it.

x > 5

Identify the scatter plot of the data. Treat the number of girls in the class as the independent variable. girls: 6, 10,10,12,15,19,20,23,25 boys: 29,14,17,30,5,9,10,22,21

1. determine which variable is on x or y axis. Girls are on x-axis 2. plot the data 3. match the graph to the one you created

Question 4: 20 pts Skip to question text. The equation of a line of best fit relating the number of cats c at an animal shelter to the number of dogs d is c = 2.1d − 26. Predict the number of cats at a shelter where there are 30 dogs.

37

the ______ ________ of a number x, written as | x |, is the distance from x to 0 on a number line

absolute value

an ______ _______ ______ is a function whose rule contains an absolute value expression.

absolute value function

a compound statement that uses the word 'and' is called a....

conjunction

Solve the equation |2m − 6 | = 10.

m = −2 or m = 8

Solve the equation |p + 5| = 3.

p = −8 or p = −2

a conjunction is true if and only if all of it's parts are true

true

a disjunction is true if and only if one of it's parts is true

true

Identify the solution of the inequality |4x + 4| > 8 and the graph that represents it.

x < −3 or x > 1 Because the absolute-value expression is greater than 8, rewrite the absolute-value inequality as a disjunction, then solve each inequality. |4x + 4| > 8 4x + 4 > 8 or 4x + 4 < −8 Rewrite the absolute value as a disjunction. 4x > 4 or 4x < −12 Subtract 4 from both sides of each inequality. x > 1 or x < −3 Divide both sides of each inequality by 4.

Identify the solution of the inequality |7p| + 36 > 15 and the graph that represents it.

all real numbers |7p| + 36 > 15 |7p| > −21 Isolate the absolute value expression. 7p > −21 or 7p < 21 Rewrite the absolute value as a disjunction. p > −3 or p < 3 Divide both sides of each inequality by 7. The solution is the set of all real numbers.

Let g(x) be the transformation of f(x) = |x| right 2 units. Identify the rule for g(x) and its graph.

g(x) = |x − 2| g(x) = f |x − h| g(x) = |x − 2| Substitute.

Let g(x) be the transformation of f(x) = |x| such that the vertex is at (2, 5). Identify the rule for g(x) and its graph.

g(x) = |x − 2| + 5 g(x) = |x − h| + k g(x) = |x − 2| + 5 Substitute.

Let g(x) be the transformation of f(x) = |x| up 3 units. Identify the rule for g(x) and its graph.

g(x) = |x| + 3 g(x) = f(x) + k g(x) = |x| + 3 Substitute.

Let g(x) be the indicated transformation of f(x) = |3x| + 4. Stretch the graph of f(x) = |3x| + 4 vertically by a factor of 3 and reflect it across the x-axis. Identify the rule and graph of g(x).

g(x) = −3|3x| − 12 f(x) = |3x| + 4 To stretch the graph vertically by a factor of 3, multiply the entire function by 3. g(x) = 3f(x) = 3|3x| + 12 To reflect the graph across the x-axis multiply the entire function by −1. g(x) = −3f(x) = −3|3x| − 12

Let g(x) be the indicated transformation of f(x) = |2x| − 5. Compress the graph of f(x) = |2x| − 5 horizontally by a factor of 1/4 and reflect it across the x-axis. Identify the rule and graph of g(x).

g(x) = −|8x| + 5 f(x) = |2x| − 5. For a horizontal compression use f ((1/b)x) where b < 1. To compress the graph horizontally by a factor of 1/4 substitute 1/4 for b in f ((1/b)x). Therefore g(x) = f(4x) = |8x| − 5 To reflect the graph across the x-axis multiply the entire function by −1. g(x) = −f(4x) = −|8x| + 5

Identify the solution of the inequality −3|n + 5| ≥ 24 and the graph that represents it.

no solutions −3|n + 5| ≥ 24 The absolute value of an expression is always positive. A negative value multiplied by a positive value is always negative. Therefore, the absolute value expression −3|n + 5| cannot be greater than or equal to a positive value. This means that −3|n + 5| ≥ 24 is a contradiction so it has no solution.

Identify the solution set of the inequality 2|f + 4| ≤ −12 and the graph that represents it.

no solutions 2|f + 4| ≤ −12 The absolute value of an expression is always positive. A positive value multiplied by a positive value is always positive. Therefore the absolute value expression 2|f + 4| cannot be less than or equal to a negative value. This means that 2|f + 4| ≤ −12 is a contradiction so it has no solution.

Solve the equation |7q| + 3 = 24.

q = 3 or q = −3

The data in the table show how long (in minutes, t) it takes several commuters to drive to work. Find the correlation coefficient and the equation of the line of best fit for the data. Treat the commute distance d as the independent variable. commute distance (miles): 20,20,20,29,34,39,29,34,50 commute time (minutes): 25,24,30,27,35,35,46,50,52

r ≈ 0.75 t ≈ 0.8d + 11.5

The data in the table show the number of boys b and girls g in several different classes. Find the correlation coefficient and the equation of the line of best fit for the data. Treat the number of girls in the class as the independent variable. girls: 5,14,16,8,10,21,25,30,29 boys: 15,10,10,19,20,23,25,12,6

r ≈ −0.18 b ≈ −0.13g + 17.9

Identify the solution of the inequality and the graph that represents it. |4x-4|/2 ≤ 4

x ≥ −1 and x ≤ 3 Isolate the absolute value expression on one side of the inequality. |4x − 4| ≤ 8 Multiply both sides by 2. Because the absolute-value expression is less than or equal to 8, rewrite the absolute-value inequality as a conjunction, then solve each inequality. 4x − 4 ≤ 8 and 4x − 4 ≥ −8 Rewrite the absolute value as a conjunction. 4x ≤ 12 and 4x ≥ −4 Add 4 to both sides of each inequality. x ≤ 3 and x ≥ −1 Divide both sides of each inequality by 4.

Identify the solution of the compound inequality −6m −4 < 2m and m − 3 ≤ −4m + 12.

−1/2 < m ≤ 3