Algebra IIA: Preparing for Quiz 2 Unit 1
The graph of an absolute value function opens up and has a vertex of (0, -3). The domain of the function is __________________. The range of the function is ___________________.
(-∞, ∞) [-3, ∞)
Which of the following is not an example of using the distributive property to multiply 12 times 22? 12(20 + 2) 22(10 + 2) 10(2 • 22)
10(2 • 22)
5(4 · 3 + 3 · 4)= 480 300 120
120
13(10 + 2) could be used to simplify which of the following problems? 130(26) 13(12) 13(20)
13(12)
8 + [13 - (2 + 1)] -3 18 20
18
5(2 + 3) ÷ 25 + 8 ÷ 4 2.25 3 12.6
3
22·23 is equal to 400 + 6 440 + 66 460 + 6
440 + 66
4[(6 - 1) + 3(5 - 2)] 44 46 56
56
18 - 5 · 3 = 3 36 39
6 ÷ 2 · 6 + 1 = 3/7 1.5 19
Select the domain and range of F. F = {(x, y ) | x + y = 10}. Domain: {10} Range: {10} Set F is not a function and does not contain a domain or range Domain: All Real Numbers Range: All Real Numbers
Domain: All Real Numbers Range: All Real Numbers
The graph of a quadratic function has a domain of (-∞, ∞) and range of [4, ∞). In two or more complete sentences, explain how the given range of the function can help you to determine whether the graph opens up or down.
The range of the function indicates that the function has a vertex at y = 4. The number on the left in the range notation is the lowest point because it is infinite. The number on the x-axis is the highest point because the number is 4. The number on the y-axis is ∞. The graph is open and have a minimum at 4. So, in conclusion, the graph goes down.
Given the function, f(x)=√x + 5 - 1, choose the correct domain written using interval notation. (-5, ∞) (-∞, -5) [-5, ∞) (-∞, -5]
[-5, ∞)
Given the function, ƒ(x) = |x - 2| + 1, choose the correct range written using interval notation. [-1, ∞) (-∞, -1] [1, ∞) (-∞, 1]
[1, ∞)
relation
a relation in which every input value has exactly one output value
Select the number property that will justify the step in the following expression. 6 + (14 + 70) = (6 + 14) + 70 = 20 + 70 = 90
associative - addition
6(3 ∙ 5) = (6 ∙ 3)5
associative - multiplication
Select the number property that will justify the step in the following expression. 2(5 • 17) = (2 • 5) 17 = 10 • 17 = 170
associative - multiplication
6 + 2 = 2 + 6
commutative - addition
Choose 2 axioms that allows 22 + (m + 8) to be written as m + 30 commutative - addition distributive associative - multiplication symmetric commutative - multiplication associative - addition identity - addition
commutative - addition associative - addition
5 ∙ 2 = 2 ∙ 5
commutative - multiplication
Choose the axiom that allows b(7) to be written 7b. commutative - addition distributive symmetric associative - multiplication commutative - multiplication
commutative - multiplication
Select the number property that will justify the step in the following expression. 4 • 13 • 25 = 4 • 25 • 13 = 100 • 13 = 1,300
commutative - multiplication
Select the number property that will justify the following expression. If cba represents three numbers multiplied together, what property allows you to rearrange the factors to read abc?
commutative - multiplication used twice
4(8 + 1) = 4 ∙ 8 + 4 ∙ 1
distributive
the range and domain of F = {(x, y ) | x + y =10}
domain = range = {all real numbers}
the range and domain of P = {(x, y) | y = 3}
domain = {all real numbers}: range = {y: y = 3}
6 + 0 = 6
identity - addition
Given the function, f(x)=√x + 1 - 6, choose the correct transformation. left 1, down 6 left 1, up 6 right 1, down 6 right 1, up 6
left 1, down 6
1/2 ∙ 2 = 1
multiplicative inverse
5 ∙ 0 = 0
property of zero
8 = 8
reflexive
Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or neither (if the set is not a relation). input -1 0 -1 -8 9 output 0 1 2 4 8 function relation neither
relation
Given the function, ƒ(x) = |x - 1| - 2, choose the correct transformation. left 1, down 2 left 1, up 2 right 1, down 2 right 1, up 2
right 1, down 2
Given the function, f(x)=√x - 2 + 3 , choose the correct transformation. left 2, down 3 left 2, up 3 right 2, down 3 right 2, up 3
right 2, up 3
If x = y, then y = x
symmetric
Select the property that allows the statement 3 = x to be written x = 3. commutative - addition distributive associative - multiplication symmetric commutative - multiplication associative - addition identity - addition
symmetric
domain
the first element of a relation or function; also known as the input value
input
the x-value of a function
The ______________________ represent the domain of a function. The _____________________ represent the range of a function.
x-values y-values
If K = {(x, y) | x - y = 5}, is Set K a function? Yes or No
yes
the domain set of C = {( 2, 5), (2, 6), (2, 7)}
{2}
Which of the following statements best represents the relationship between a relation and a function. A function is always a relation but a relation is not always a function. A relation is always a function but a function is not always a relation. A relation is never a function but a function is always a relation.
A function is always a relation but a relation is not always a function.
Select the sets that are not functions. A = {(1, 2), (2, 3), (3, 4), (4, 5)} B = {(1, 2), (2, 1), (3, 0), (4, -1)} C = {(-1, 3), (0, 3), (1, 3), (2, 3)} D = {(1, 1), (1, 2), (1, 3), (1, 4)} E = {(6, 2), (7, 3), (6, -1), (5, 4)}
D = {(1, 1), (1, 2), (1, 3), (1, 4)} E = {(6, 2), (7, 3), (6, -1), (5, 4)}
If the relation is a function, list the domain and range. If the relation is not a function, choose "not a function". C = {(9, 1) (8, -3) (7, 5) (-5, 3)} Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3} Domain: {1, -3, 5, 3} Range: {9, 8, 7, -5} not a function
Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3}
Which of the following are true of F(x)? F(x) is read as "F of x" F(x) is the horizontal distance on the graph. F(x) is the graph at a particular value of x. F(x) is a whole number. y is equal to F(x)
F(x) is read as "F of x" F(x) is the graph at a particular value of x. y is equal to F(x)
function
any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane
10 + (3 + 2) = (10 + 3) + 2
associative - addition
Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or neither (if the set is not a relation). A = {(1, 2) (2, 2) (3, 2) (4, 2)} relation function neither
function
Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or neither (if the set is not a relation). F = {(x, y ) | x + y = 10} relation function neither
function
8 ∙ 1 = 8
identity - multiplication
Given the function, ƒ(x) = 1/x+1 - 5, choose the correct transformation. left 1, down 5 left 1, up 5 right 1, down 5 right 1, up 5
left 1, down 5
range
the second element of a relation or function; also known as the output value
output
the y-value of a function
If x = y and y = 7, then x = 7
transitive
If K = {(x, y)|x - y = 5}, find the corresponding range of y for the domain {0, 2, 4}. {-5, -3, -1} {0, 2, 4} {5, 7, 9}
{-5, -3, -1}
the range set of E = {(3, 3), (4, 4), (5, 5), (6, 6)}
{3, 4, 5, 6}
Choose the function that shows the correct transformation of the quadratic function shifted eight units to the left and one unit down. ƒ(x) = (x - 8)2 - 1 ƒ(x) = (x - 8)2 + 1 ƒ(x) = (x + 8)2 - 1 ƒ(x) = (x + 8)2 + 1
ƒ(x) = (x + 8)2 - 1
Choose the function that is a "parent function". ƒ(x) = x + 3 ƒ(x) = (x - 3)2 ƒ(x) = √x ƒ(x) = |x - 3|
ƒ(x) = √x