1st Semester Review (Algebra)

Use the equation f(x) = -5x - 8 to determine the range for the domain ( 1, 4, 7).

(-43, -28, -13)

Use the equation f(x) = 4x + 1 to determine the range for the domain (2, 3, 5).

(9, 13, 21)

What is the slope of the equation: y = -x - 14

-1

What is the x-intercept for the equation -3x + y = 3

-1

What is the slope of the line?

-1/2

x= 5

-10x + 2= -8x - 8

x= 7

-13 + 4x = 1 + 2x

x= 11

-14 - 3x= -5x + 8

What is the Y-intercept for the equation 2x - 5y = 10

-2

What is the x-intercept for the equation -2x + y = 4

-2

What is the x-intercept for the equation 3x + 2y = -6

-2

What is the y-intercept of the graph?

-2

The slope of a line passing through (0,-4) and (5,6)

-2/5

What is the y-intercept for the equation 3x + 2y = -6

-3

What is the y-intercept of the table?

-3

Find the 2nd, 5th, and 9th terms of the following sequence: A(n) = -9 + (n-1)(6)

-3, 15, 39

x= -4

-3x - 15= -6x - 27

x= -5

-5x + 2= 4x + 47

x= -2

-6x + 20= -2x + 28

The ordered pairs are for the same direct variation. Find the missing value. (-1,2) and (4,y)

-8

x= 3

-8 - x= -4x +1

Find the common difference: .7, 1.5, 2.3, 3.1, ...

.8

What is the y-intercept of the equation: y=5x

0

What is the y-intercept of the graph?

0

Which steps should be used to graph the equation y - 4 = 1/3 (x + 2)?

1. Plot the point (-2,4). 2. From that point, count left 3 units and down 1 unit and plot a second point. 3. Draw a line through the two points.

What is the constant of variation in this equation: 2x = 4y

1/2

Your dryer has 3 shirts, 4 sweatshirts, and 5 towels. If you pull out two items, one item at a time, what is the probability you pull out two shirts?1

1/22

The amount of blood in a person's body varies directly with body weight. A person who weighs 160 lbs has about 5 qt. of blood. What is the constant of variation?

1/32

The slope of a line passing through (4,6) and (-2,5)

1/6

The ordered pairs are for the same direct variation. Find the missing value. (3,4) and (9,y)

12

The points (3,8) and (2,y) are two points on the graph of an inverse variation. Find the missing value.

12

What is the constant of variation in this equation: xy = 12

12

A bus traveling at an average rate of 30 mph left the city at 11:45 am. A car following the bus at 45 mph left the city at noon. At what time did the car catch u with the bus?

12:30 pm

x= 4

13 - 4x= 1 - x

Determine the constant of variation for a direct variation if y = 75 and x = 5.

15

x= 1/2

15x - 10= -9x + 2

Find the 2nd, 5th, and 9th terms of the following sequence: A(n) = 8 + (n-1)(9)

17, 44, 80

Calculate the mean of the following numbers: 14.6, 19.7, 22.5, 16.9, 18.2

18.38

Matt drives to work. Because of traffic condition, he averages 22 mph. he returns home averaging 32 mph. The total travel time is 2.25 hrs. Based on this, how long does it take him to drive to work?

1:20

A jet leaves the Chicago, IL airport traveling at an average rate of 564 km/h. Another jet leaves the airport one half hour later traveling at 744 km/h in the same direction. How long will it take the second jet to overtake the first?

1:34

What is the slope of the equation: y =2x + 3

2

Two bicyclists ride in opposite directions. The speed of the first bicyclist is 5 miles per hour faster than the second. After 2 hours they are 70 miles apart. What is the rate of the faster rider?

20 mph

Nick and Gavin leave their home traveling in opposite directions on a straight road. Nick drives 20 mph faster than Gavin. After 4 hours they are 250 miles apart. Based on this, what is Gavin's rate?

21.25 mph

If you roll two six-sided dice, what's the probability of not rolling a five on either die?

25/36

At 1:30 pm, Tome leaves in his boat from a dock and heads south. He travels at a rate of 25 mph. 10 minutes later, Mary leaves the same dock in her speedboat and heads after Tom. If she travels at a rate of 30 mph, when will she catch up with Tom?

2:30 pm

y = (-1/2)x - 3

2x + 4y = -12 (Write in slope-intercept form)

x= -8

2x + 7= 4x + 23

y = -2x +5

2x + y = 5 (Write in slope-intercept form)

x= 12

2x - 1= x + 11

x= 9

2x - 5= x + 4

x= 8

2x= 4x - 16

What is the y-intercept for the equation -3x + y = 3

3

What is the y-intercept of the equation: y= 2x + 3

3

Find the next two terms in each sequence: 2, 2 1/4, 2 1/2, 2 3/4, 3, ...

3 1/4, 3 1/2

Determine the constant of variation for an inverse variation if y = 75 and x = 5.

375

Write an expression for the following statement: 5 less than 3 times a number

3n - 5

y = (-3/2)x + 3

3x + 2y = 6 (Write in slope-intercept form)

y = -x - 4

3x + 3y = -12 (Write in slope-intercept form)

x= -25

3x + 8= 2x - 17

y = (1/2)x - 3/2

3x - 6y = 9 (Write in slope-intercept form)

Find the common difference: -7, -3, 1, 5, ...

4

What is the slope of the table?

4

What is the y-intercept for the equation -2x + y = 4

4

The sum of four consecutive integers is 170. What are the integers?

41, 42, 43, 44

b= 10

42 + 7b= 8(b + 4)

Evaluate (4x²)³ - 6y if x = 3 and y = 4

46632

y = (-1/3)x - (1/2)

4x + 12y = -6 (Write in slope-intercept form)

y = (-4/7)x + 6/7

4x + 7y = 6 (Write in slope-intercept form)

y = -4x - 2

4x + y = -2 (Write in slope-intercept form)

x= 3

4x - 40= 7(-2x + 2)

The ordered pairs are for the same direct variation. Find the missing value. (2 , 5) and (x , 12.5)

5

What is the slope of the equation" y=5x

5

What is the x-intercept for the equation 2x - 5y = 10

5

x= 1

5 + 3x= 2x + 6

What is the slope of the line?

5/2

What is the slope of the graph?

5/3

The sum of two consecutive odd integers is 116. What are the integers?

57 and 59

y = (-5/3)x - 8/3

5x + 3y = -8 (Write in slope-intercept form)

y = (5/4)x - 7/4

5x - 4y = 7 (Write in slope-intercept form)

Find the common difference: 4,10,16,22,...

6

The points (4,12) and (x,8) are two points on the graph of an inverse variation. Find the missing value.

6

The weight needed to balance a lever varies inversely with the distance from the fulcrum to the weight. If Matt weighs 180 lbs and is 6 feet from the fulcrum, where should Sam sit if he weighs 160 lbs?

6.75 feet

The sum of three consecutive even integers is 192. What are the integers?

62, 64, 66

x= -6

6x + 7= 13 + 7x

y = 2x - 2

6x - 3y = 6 (Write in slope-intercept form)

x= -3

6x - 8= 9x + 1

y = (2/3)x - 1

6x - 9y = 9 (Write in slope-intercept form)

What is the constant of variation in this equation: y = 7x

7

What is the slope of the table?

7

What is the y-intercept of the graph?

7

What is the y-intercept of the table?

7

x= -9

75 + 14x= 4x - 15

x= 15

7x - 12= 3 + 6x

y = 7x - 13

7x - y = 13 (Write in slope-intercept form)

Calculate the median stay for these patients: 17, 3, 4, 25, 8, 7, 13, 10, 5, 11, 9, 21, 3, and 1.

8.5

y = (-8/3)x - 5

8x + 3y = -15 (Write in slope-intercept form)

x= 1

8x + 4= 10 + 2x

y = -8x - 5

8x + y = -5 (Write in slope-intercept form)

x= 14

8x - 16= 4x + 40

x= 7

8x= 3x + 35

y = (-9/4)x - 1

9x + 4y = -4 (Write in slope-intercept form)

2.25

A 3.2 m ladder is leaning against a wall with its foot 1.5 m from the wall. How far is a second ladder from the wall if it is 4.8 m long and parallel to the first ladder?

12.5

A building casts a shadow 37.5 m long. If a metre stick casts a shadow 3 m long at the same time and location, how tall is the building?

discrete graph

A graph of isolated points

continuous graph

A graph with no breaks in it

arithmetic sequence

A numerical pattern that increases or decreases at a constant rate or value.

8

A painting is 2 in. tall and 4 in. wide. If it is enlarged to a width of 16 in. then how tall will it be?

8.4

A person whose eye height is 1.2 m stands 0.4 m from a mirror. If the mirror is 2.8 m from the wall when the person sees the top of the wall, how tall is the wall?

32.5

A person whose eye height is 1.5 m stands 0.3 m from a mirror and sees the top of a building in the mirror. If the mirror is 6.5 m from the wall, how tall is the wall?

20

A person whose eye height is 1.6 m stands 0.8 m from a mirror. If the mirror is 10 m from a wall when the person sees the top of the wall, how tall is the wall?

function

A relation in which every domain or input value has exactly one range or output value

ordered pair

A set of numbers, or coordinates, written in the form (x,y)

Vertical Line Test

A visual method used to determine whether a graph represents a function or not.

11

ABC ~ DEF

20

ABC ~ DEF........ Find d if b = 6, e = 15, and a = 8.

What property is used in the following example: 5 + -7 = -7 + 5 ?

Cummutative Property of Addition

Determine if the following points represent a direct or inverse variation: (3,12), (5,20), (8,32).

Direct Variation

8.25

Find a if b = 11, e = 8, and d = 6.

11

Find f(x) = (1/2)x +7 when x=8

126

Find f(x) = 10x+6 find f(12)

10

Find the height of the flag pole in m.

3

Find the length of x

m = 1/4

Find the slope using the given table

-8

Find x for f(x) = 5x - 6 when f(x) = -46

coordinate plane

Formed by the intersection of two number lines, the horizontal axis and the vertical axis.

Function

Function or Not a Function?

Not a Function

Function or Not a Function?

Exponential Function family

Graphs are J-shaped curves; have no maximums or minimums; have equation form f(x) = a^x (a number raised to the X power)

Quadratic Function family

Graphs are U-shaped curves; increase and decrease across the Domain (x axis); have a maximum or minimum; have a equation form f(x) = x^2 (X raised to the 2 power)

Linear Absolute Value Function family

Graphs are V-shaped lines; increase and decrease over the Domain (x axis); have a maximum or a minimum; have an equation form f(x) = |x|

Linear Piece-wise Function family

Graphs are pieces of Lines put together to make one picture (look like Zig-Zags); have equation form f(x) = 2x, -3x +5, and -9 (two or three equations in one)

Non-Function family

Graphs that FAIL the Vertical Line Test.

Linear Function family

Graphs that are lines that increase or decrease; have no maximums or minimums; have equation form f(x) = mx + b

By the steepness. The steeper the line the faster the speed.

How can tell you which line indicates a faster speed?

30 Seconds

How much time does it take for the skier to go back to the ski lodge?

What property states that a number multiplied by one is that number?

Identity Property of Multiplication

vertical line test

If any vertical line passes through no more than one point of the graph of a relation, then the relation is a function.

On a graph, how can you tell if you have a negative slope?

If the line is going down or decreasing

How do you use the vertical line test to determine whether a graph is a function?

If the line touches the graph in more that one spot, it is not a function.

3

If the slope is -3/4, how many units do you rise?

Mapping

Illustrates how each element of the domain is paired with an element in the range.

9

In the equation y= -9x + 9, what is the y-intercept?

-9

In the equation y= -x + 9, what is the slope?

m

In the linear equation (y = mx + b) which value is the slope?

b

In the linear equation (y = mx + b) which value is the y-intercept?

Determine if the following points represent a direct or inverse variation: (3,12), (6,6), (9,4).

Inverse Variation

Type of Slope

Negative

If a relation is a function, can you have two outputs associated with the same input?

No

Is this a function: (2,5) , (4, 9), ( 2, 7) , ( 7, 12)

No

Is this an arithmetic sequence: 2, 4, 8, 16, 32, ...

No

Is this equation a direct variation: 6x + 7y = 8

No

y=5

No x intercept . (0 , 5)

stopped

On a distance time graph, a horizontal line indicates the object's motion is

constant

On a distance time graph, a straight diagonal line indicates the object's speed is

Type of slope

Positive

Vertical Change

Rise

Slope

Rise over Run

Horizontal Change

Run

y = 2/3x

Slope of 2/3, y intercept of 0

x = -0.8

Solve for x.

x = -5.2

Solve for x.

x = 1.33

Solve for x.

x = 10.2

Solve for x.

x = 13

Solve for x.

x = 14

Solve for x.

x = 2

Solve for x.

x = 24

Solve for x.

x = 3

Solve for x.

x = 4.5

Solve for x.

x = 5

Solve for x.

x = 8

Solve for x.

Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use: Step 1: Choose a point on the line, such as (2, 5). Step 2: Choose another point on the line, such as (1, 3). Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is 1/2 Step 4: Substitute those values into the point-slope form. y - y1 = m(x - x1) y - 3 = (x - 1) Which of Talia's steps is incorrect?

Step 3 is incorrect because it shows an incorrect ratio for the slope.

The range of a function pertains to which variable?

The dependent variable or y

The domain of a function pertains to which variable?

The independent variable or x

domain

The set of all input values

range

The set of all output values

Anya graphed the line (y - 2) = 3(x - 1) on the coordinate grid.

The slope of her line is 3

The person returns to where they started.

What happens between 2 to 4 seconds?

car is stopped

What is happening on the graph from B to C?

15

What is the length of yz?

0 Slope

What is the slope of a horizontal line?

m = 1/4

What is the slope of a line passing through (-24, 9) and (24, 21)?

m = -1/3

What is the slope of a line passing through (7, 2) and (10, 1)?

Undefined Slope

What is the slope of a vertical line?

m = -5

What is the slope of this line: y = -5x - 1

m = 7

What is the slope of this line: y = 7x + 5

Absolute Value

What type of graph is this?

Cube root

What type of graph is this?

Cubic

What type of graph is this?

Linear Graph

What type of graph is this?

Quadratic

What type of graph is this?

Square root

What type of graph is this?

The equation of a linear function in point-slope form is y - y1 = m(x - x1). Harold correctly wrote the equation y = 3(x - 7) using a point and the slope. Which point did Harold use?

When Harold wrote his equation, the point he used was (7, 0).

B-C

Which line segment in the graph shows the object is not moving

The green line (not very steep)

Which line shows a slow, constant speed?

The red line (horizontal)

Which line shows that the object is not moving?

The orange line (steepest)

Which line shows the fastest speed?

If a relation is a function, can you have two inputs associated with the same output?

Yes

Is this a function: (3,9) , ( 4,7) , (2,12), (7, 9)

Yes

Is this an arithmetic sequence: .2, -.6, -1.4, -2.2, ...

Yes

Is this equation a direct variation: 5x + 2y = 0

Yes

On a speed/time graph, what does it mean when you have a horizontal line?

You are traveling at a constant speed

continuous graph

a graph made up of connected lines or curves

discrete graph

a graph made up of unconnected points

dependent variable

a quantity or variable that depends on another quantity or variable; always labeled on the Y axis

independent variable

a quantity or variable that does not depend on anything; always labeled on the X axis

function

a relation in which each element of the domain is paired with exactly one element of the range

relation

a set of ordered pairs

relation

a set of ordered pairs; a mapping between a set of inputs and a set of outputs

function notation

an equation in the form of 'f(x)=' to show the output value of a function, f, for an input value x

1

f(x) = (1/10)x+3 find f(-20)

24

f(x) = -10x + 4 find f(-2)

Which linear function represents the line given by the point-slope equation y + 1 = -3(x - 5)?

f(x) = -3x + 14

Which equations and/or functions represent the graphed line? Check all that apply.

f(x) = 0.5x + 2 f(x) = 1/2x + 2 y - 3 = 1/2(x - 2) y - 1 = 0.5(x + 2)

What is the function rule for the total cost f(x) of x books, if each book cost $11.95?

f(x) = 11.95x

What is the function rule for the amount of change f(x) you receive from a $50 bill if you buy x pounds of dog food at $1.60 a pound?

f(x) = 50 - 1.6x

0

f(x) = 5x + 10 find f(-2)

-31

f(x) when f(x) =3x - 7 find f(-8)

13

find f(6) + g(14) when f(x) = (1/2)x + 5 and g(x) = (1/14)x + 4

81

find f(x)=3^x when x=4

17

find x for f(x) = -x+10 when f(x) = -7

-10

find x for f(x) =-4x - 8 when f(x) = -48

How do you calculate k (the constant of variation) for inverse variation?

k = xy

How do you calculate k (the constant of variation) for direct variation?

k = y/x

In the slope-intercept form, which letter represents slope?

m

Quadrants

the four sections of the coordinate plane

origin

the point (0,0) where the x-axis and the y-axis intersect in a coordinate plane

domain

the point of the first numbers (x-values) of the ordered pairs in the relation

range

the set of second numbers y-values of the ordered pairs in a relation

Slope

the steepness of a line

zeros

the values of x that make a quadratic equation equal zero

The point (0,-6) is

the y intercept of -6

The point (0,4) is

the y intercept of 4

decreasing at an increasing rate

top right, rainbow line starting from the top

f(x) = (-1/4)x + 2

write a function for the graph shown

x= 6

x + 2= =14 - x

y = (-1/5)x + 12/5

x + 5y = 12 (Write in slope-intercept form)

y = (1/3)x + 3

x - 3y = -9 (Write in slope-intercept form)

y = (1/6)x + 2

x - 6y = -12 (Write in slope-intercept form)

2x - 5 = 8x + 1

x = -1

2x - 5 = 4x - 1

x = -2

3x + 8 = 2x - 17

x = -25

6x - 8 = 1 + 9x

x = -3

8x + 4 = 10 + 2x

x = 1

15x - 10 = -9x + 2

x = 1/2

3x - 5 = 2x + 5

x = 10

2x - 1 = x + 11

x = 12

x - 15 = 13 - 6x

x = 4

7x - 17 = 4x + 1

x = 6

The equation of a vertical line passing through (8,-4)

x = 8

2x - 5 = x + 4

x = 9

To find the y-intercept, plug 0 in for the _________________.

x-coordinate

-5x - 5 = 75+0x

x= -16

-7x + 4 = -10x -14

x= -6

-15x - 40 = 23 - 8x

x= -9

2x + 5 = 7 + 0x

x= 1

-14 - 3x = -5x + 8

x= 11

4x + 4 = 2x + 36

x= 16

-30x + 0 = -27x - 63

x= 21

5x - 26 = 18x +0

x=2

63 - x = 2x + 3

x=20

Suppose y varies inversely with x and y = -3 when x = 7. Write an equation for the inverse variation.

xy = -21

Suppose y varies inversely with x and y = 8 when x = 7. Write an equation for the inverse variation.

xy = 35

Which equation represents a line that passes through (2, -1/2) and has a slope of 3?

y + 1/2 = 3(x - 2)

Which equation represents a line that passes through (-9, -3) and has a slope of -6?

y + 3 = -6(x + 9)

What is the equation of the graphed line in point-slope form?

y + 3 = 2 (x + 3)

What is the equation of the graphed line in point-slope form?

y + 6 = 3/4 (x + 4)

Which equation represents a line that passes through (5, 1) and has a slope of 1/2 ?

y - 1 = 1/2(x -5)

What is the equation of the graphed line in point-slope form?

y - 1 = 2/3 (x - 3)

Which equation represents a line that passes through (4,1/3 ) and has a slope of 3/4 ?

y - 1/3 = 3/4 (x - 4)

Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3 ?

y - 2 = 1/3(x - 3)

Alejandra correctly wrote the equation y - 3 = 1/5 (x - 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?

y - 3 = 2(x - 10)

Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?

y - 4 = 2/5(x + 2)

Chin was shown the graph of a line that contained point (1, 7). He wrote f(x) = 4x + 3 to correctly represent the line. Which of these equations could represent the same line?

y - 7 = 4(x - 1)

The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x = 0 representing the year 2000, the graph below models this scenario. What number will complete the point-slope equation that models this scenario?

y 50,000 = -3,000 (x 10)

Write an equation for the following points: ( -1, 7), (0, 5), (1, 3)

y = -2x + 5

Write an equation for the following points: (-1,-2), (0,-4), (1,-6), (2,-20), (3,-58)

y = -2x^3 - 4

What is the equation of the graph in slope intercept form?

y = -3x

Slope intercept form of equation given a slope of -4 and y-intercept of -2

y = -4x-2

Slope = -8 and y intercept = 5

y = -8x + 5

Write an equation of a line with a Slope of -8 and y intercept of 5

y = -8x + 5

Write an equation for the following points: (-1,2), (0,3), (1,2), (2, -1), (3,-6)

y = -x^2 + 3

Slope intercept form of equation given a slope of 2/3 and y-intercept of 5

y = 2/3x+5

Write an equation of the direct variation that includes the point (7,2)

y = 2/7 x

Slope = 2/7, y intercept = 5 in slope intercept form

y = 2/7x + 5

Write an equation of a line where the Slope = 2/7 and y intercept = 5 in slope intercept form

y = 2/7x + 5

Write an equation of the direct variation that includes the point (2,7)

y = 3.5x

What is the equation of the graph in slope intercept form?

y = 3/2x

Write an equation of a line that passes through the points (0,-2) and (4,1) in slope intercept form

y = 3/4x - 2

through (0,-2) and (4,1) in slope intercept form

y = 3/4x - 2

Suppose y varies inversely with x and y = 4 when x = 9. Write an equation for the inverse variation.

y = 36/x

Slope = 0, y intercept = 4

y = 4

Write an equation of a line where the Slope = 0, y intercept = 4

y = 4

Slope = 4/3, y intercept = 3

y = 4/3x + 3

Write an equation of a line where the Slope = 4/3 and y intercept = 3

y = 4/3x + 3

Write an equation for the following points: (0,2), (1,6), (2,10)

y = 4x + 2

Slope = 5/3, y intercept = -4 in slope intercept form

y = 5/3x - 4

Write an equation of a line where the Slope = 5/3, y intercept = -4 in slope intercept form

y = 5/3x - 4

What is the equation of the graph in slope intercept form?

y = 5/3x -2

What is the slop-intercept form?

y = mx + b

Write an equation for the following points: ( 0,6), (1, 7), (2, 10), (3,15)

y = x^2 + 6

Write and equation for the following points: (-1,1), (0,2), (1,3), (2,10), (3,29)

y = x^3 + 2

To find the x-intercept, plug 0 in for the __________________.

y-coordinate

The equation of a horizontal line passing through (-2,4)

y=4

function

{(3,5) (10,5) (4,5) (8,5) (-1,5)}

function

{(3,5) (10,7) (4,3) (8,5) (-1,5)}

function

{(3,5) (10,7) (4,3) (8,5) (-3,5)}