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Algebra

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Graph each function. Identify the domain and range. ? 1.? ? SOLUTION:?? ? The function is defined for all real values of x, so the domain is all real numbers. ? D = {all real numbers} ? The y-coordinates of points on the graph are real numbers less than or equal to 4, so the range is . ? ANSWER:?? D = {all real numbers}; ? 2.? ? SOLUTION:?? ? The function is defined for all real values of x, so the domain is all real numbers. ? D = {all real numbers} ? The y-coordinates of points on the graph are real numbers between 8 and ?2 and less than or equal to ?8, so the range is . ANSWER:?? D = {all real numbers}; ? Write the piecewise-defined function shown in each graph. ? 3.? ? SOLUTION:??

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1.?OCEANS The table shows the temperature in the ocean at various depths. ? ? a. Make a scatter plot and a line of fit, and describe the correlation. ? b. Use two ordered pairs to write a prediction equation. ? c. Use your prediction equation to predict the missing value. ? SOLUTION:?? a. ?????? ?????????????????????????? [0, 3000] scl 500 by [0, 25] scl 1 Since the slope of the line is negative, the correlation is negative. ? b. Consider the ordered pairs (0, 22) and (2000, 6). ? ? ????????????? Substitute m = ?0.008 and (x, y) = (0, 22) in the slope-intercept form. ? ? Substitute m = ?0.008 and b = 22 in the slope-intercept form. ? c. Substitute x = 2500 in the prediction equation . ? ?

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Write an equation in slope-intercept form for the line described. ? 1.?slope 1.5, passes through (0, 5) SOLUTION:?? Substitute m = 1.5 and (x, y) = (0, 5) in the equation y = mx + b. ? ? Substitute m = 1.5 and b = 5 in the equation ? y = mx + b. ? ANSWER:?? y = 1.5x + 5 2.?passes through (?2,?3)?and?(0,?1)??????????????? SOLUTION:?? Substitute ?and? ?in?the?slope?formula? . ? ? Substitute m = ?1 and ?in?the?point?slope?form? . ? ? ANSWER:?? y = ?x + 1 3.?passes through (3, 5); m = ?2 SOLUTION:?? Substitute m = ?2 and (x, y) = (3, 5) in the equation y = mx + b. ? ? Substitute m = ?2 and b = 11 in the equation ? y = mx + b. ? y = ?2x + 11 ANSWER:?? y = ?2x + 11 4.?passes through (?8, ?2); SOLUTION:??

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CCSS?REGULARITY??Find?the?rate?of?change?for?each?set?of?data. ? 1.? SOLUTION:?? Use the ordered pairs (4, 24) and (6, 36). ? ? The rate of change is 6 feet/min. ANSWER:?? 6 feet/min 2.? SOLUTION:?? Use the ordered pairs (10, 32) and (15, 48). ? ? The rate of change is 3.2 cm 3 /sec. ANSWER:?? 3.2 cm 3 /sec 3.? CAMERAS The graph shows the number of digital still cameras and film cameras sold by Yellow Camera Stores in recent years. ? a. Find the average rate of change of the number of digital cameras sold from 2004 to 2009. ? b. Find the average rate of change of the number of film cameras sold from 2004 to 2009. ? c. What do the signs of each rate of change represent? SOLUTION:??

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State whether each function is a linear function. Write yes or no. Explain. ? 1.? SOLUTION:?? A linear function is a function with ordered pairs that satisfy a linear equation of the form y = mx + b. The function ?is?linear?as?it?can?be?written?as? . ANSWER:?? Yes; it can be written as 2.? SOLUTION:?? A linear function is a function with ordered pairs that satisfy a linear equation of the form y = mx + b. ?cannot?be?written?in?the?form?f (x) = mx + b. ? So the function is not linear. ANSWER:?? No; it cannot be written as f (x) = mx + b. 3.? SOLUTION:?? is not a linear function as x has an exponent that is not 1. ANSWER:?? No; x has an exponent that is not 1. 4.? SOLUTION:??

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CCSS?STRUCTURE??State?the?domain?and?range?of?each?relation.?Then?determine?whether?each?relation is a function . If it is a function, determine if it is one-to-one, onto, both, or neither. ? 1.? SOLUTION:?? The?left?side?of??the?mapping?is?the?domain?and?the?right?side?is?the?range.The?members?of?the?domain?are?the?x- values of the relation while the members of the range are the y-values. ? D = {?2,?5,?6},?R?=?{??8, 1, 3}; ? Each element of the domain is paired with exactly one element of the range. So, the relation is a function. ? The function is both one-to-one and onto because each element of the domain is paired with a unique element of the range and each element of the range corresponds to an element of the domain. ANSWER:??

Matrices

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Algebra
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Multiplying Matrices: Procedure and Application A. Satterwhite 2007 Multiply Matrices: The Basics 3 -3 0 2 2 -2 -2 1 4 5 6 = Multiply the elements of each ROW of the 1st matrix by the respective elements in each COLUMN of the 2nd matrix. Add the products. Enter that sum into the element in the particular row and column used. ( )( )+( )( )+( )( ) ( )( )+( )( )+( )( ) ( )( )+( )( )+( )( ) ( )( )+( )( )+( )( ) 2 4 -1 0 3 1 5 2 6 3 -1 1 2 -1 3 1 5 2 4 -1 0 3 1 6 2 2 6 0 -1 -1 1 3 3 1 4 5 3 13 6 2 Matrix Multiplication Example: 2x3 3x2 = Implications: 3 -3 0 2 2 -2 -2 1 4 5 6 3 4 2 3 13 3 x 2 2 x 2 3 x 2

Algebra 1 Quiz: Rates, Ratios, & Proportions

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Algebra
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1. If Carl can paint 3 walls in 5 hours and Jane can paint 2 walls in 3 hours. How long would it take for both of them to paint 1 wall? 2. It takes pipes working together 4 hours to fill 1 tank. How long would it take to fill 3/8 of a tank? 3. Jack can fix a table in 6 hours. Jack and Stacey can fix a table in 2 hours. How fast can Stacey fix a table? 4. Jimbo can chop down 2 trees in 5 hours. Gumbo can chop down 1 tree in 3 hours. Jimbo, Gumbo and Alex can chop down a tree in 1 hour. How fast can Alex chop down 1 tree? NAME: DATE:
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Algebra 1 Quiz: Inequalities & Rates

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1. If 3 < 2y-1 < 13 , What is the sum of the greatest integer value of y and the least integer value of y? 2. How many integers are there between -100 and 100, inclusive? 3. Solve for x! 3(2x + 4) > 4x + 10 4. Suppose one painter can paint a house in 4 hours, and the second painter takes 2 hours to paint a house. How long would it take the two painters together to paint the house? Extra Credit 5. If six men can do a job in fourteen days, how many would it take to do the job in twenty-one days? NAME: DATE:
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Algebra 1 Quiz: Inequalities & Consecutive Integers

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1. Graph the following inequality. : y x + 3 2.Graph the following inequality: y > 2x ? 1 3.The sum of three consecutive even integers is 18. Find the second integer. 4. Find three consecutive odd integers such that the sum of the second and third integers is four times the first. 4. CHALLENGER An electronics store sells DVD players and cordless telephones.? The store makes a $75 profit on the sale of each DVD player (d) and a $30 profit on the sale of each cordless telephone (c).? The store wants to make a profit of at least $255 from its sales of DVD player and cordless telephones.? Which inequality describes this situation? A. 75d + 30c < 255 B. 75d + 30c < 255 C. 75d + 30c > 255 D. 75d + 30c > 255 NAME: DATE:

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