coordinate algebra semester 1 review
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Coordinate Algebra Semester 1 Review. UNIT 3 – Linear & Exponential Functions. Question 1 Function vs. Relation. Is this a function? (-1, 2), (8, -4), (12, 3), (12, -3). Question 1 Function vs. Relation. Is this a function? (-1, 2), (8, -4), (12, 3), (12, -3). No, 12 has two outputs. - PowerPoint PPT PresentationTRANSCRIPT
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Coordinate AlgebraSemester 1 Review
UNIT 3 – Linear & Exponential Functions
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Question 1 Function vs. Relation
Is this a function?(-1, 2), (8, -4), (12, 3), (12, -3)
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Question 1 Function vs. Relation
Is this a function?(-1, 2), (8, -4), (12, 3), (12, -3)
No, 12 has two outputs.
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Question 2 Function vs. Relation
Is this a function?
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Question 2 Function vs. Relation
Is this a function?
Yes, each input has one output..
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Question 3 Evaluate Functions
Evaluate f(x) = 5(3x) + 1 for x = 3.
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Question 3 Evaluate Functions
136
Evaluate f(x) = 5(3x) + 1 for x = 3.
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Question 4 Combining Functions
2 2If 6 3 5 and 4 5 8,
find .
f x x x g x x x
g f x
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Question 4 Combining Functions
2 2If 6 3 5 and 4 5 8,
find .
f x x x g x x x
g f x
22 8 13x x
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Question 5 Exponential, Linear, or Neither
Each term in a sequence is exactly ½ of the previous term.
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Question 5 Exponential, Linear, or Neither
Each term in a sequence is exactly ½ of the previous term.
Exponential.
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This function is decreasing at a constant rate.
Question 6 Exponential, Linear, or Neither
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This function is decreasing at a constant rate.
Question 6 Exponential, Linear, or Neither
Linear
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Question 7
What is happening to y as x increases for the graph?
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
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Question 7
y decreases
What is happening to y as x increases for the graph?
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
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Question 8
Find the rate of change: f x =-2x+4 1 2when x =2 and x =-3
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Question 8
2ROC
Find the rate of change: f x =-2x+4 1 2when x =2 and x =-3
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Question 9
Write an explicit and recursive rule for the nth term. Find a50.
1, 5, 9, 13, …
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Question 9
1 1
50
exp : 4 3
: 1, 4
197
n
n n
licit a n
recursive a a a
a
Write an explicit and recursive rule for the nth term. Find a50.
1, 5, 9, 13, …
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Question 10
Write an explicit and recursive rule for the nth term. Find a8.
8, 16, 32, 64,…
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Question 10
1
1 1
8
exp : 8(2)
: 8, 2
1024
nn
n n
licit a
recursive a a a
a
Write an explicit and recursive rule for the nth term. Find a8.
8, 16, 32, 64,…
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Describe the domain:
Question 11
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
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Describe the domain:
Question 11
( , )-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
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What is the asymptote for the function?
Question 12
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
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What is the asymptote for the function?
Question 12
2y-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
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Compare the y-intercepts of the following two functions.
Question 13
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Compare the y-intercepts of the following two functions.
Question 13
( )
int (0,1)
( )
int (0,5)
g x hasa smaller
y ercept at
and f x hasa greater
y ercept at
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Is this function discrete or continuous?
Question 14
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Is this function discrete or continuous?
Question 14
discrete
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Given the graph, which of the following are true?
Question 15
A. I and IIB. I and IIIC. I and IVD. I, II, and IV
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Given the graph, which of the following are true?
Question 15
A. I and IIB. I and IIIC. I and IVD. I, II, and IV
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If the graph of f(x) is,
What does –f(x) look like?
Question 16
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If the graph of f(x) is,
What does –f(x) look like?
Question 16
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Ely decides to join a gym. Buff Bodies charges $50 sign-up fee plus $30 a month. Mega Muscles charges $10 sign-up fee plus $40 a month.
Write a function for the cost of each gym membership.
Question 17
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Ely decides to join a gym. Buff Bodies (B) charges $50 sign-up fee plus $30 a month. Mega Muscles (M) charges $10 sign-up fee plus $40 a month.
Write a function for the cost of each gym membership.
Question 17
( ) 30 50
( ) 40 10
Bx x
M x x
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Ely decides to join a gym. Buff Bodies charges $50 sign-up fee plus $30 a month. Mega Muscles charges $10 sign-up fee plus $40 a month.
Will these two functions ever intersect? If so, where? What does this mean?
Question 18
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Ely decides to join a gym. Buff Bodies charges $50 sign-up fee plus $30 a month. Mega Muscles charges $10 sign-up fee plus $40 a month.
Will these two functions ever intersect? If so, where? What does this mean?
Question 18
(4,170)
4 ,
arg .
After months they will
ch e the same amount
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For Christmas you get an iPhone 5 worth $800. Every month the value decreases by 5% with all the new products coming out.
a) Write an exponential equation describing the situation.
b) How much is the phone worth in 3 years?
Question 19
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For Christmas you get an iPhone 5 worth $800. Every month the value decreases by 5% with all the new products coming out.
a) Write an exponential equation describing the situation.
b) How much is the phone worth in 3 years?
Question 19
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Matt made $3,000 last summer coach tennis camps. He wants to continue this business in the following years. He hopes that his profit will increase 12% each year.
Write an equation to describe this situation.
What is the growth/decay factor?
How much will he make in 4 years?
Question 20
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Matt made $3,000 last summer coach tennis camps. He wants to continue this business in the following years. He hopes that his profit will increase 12% each year.
Write an equation to describe this situation.
What is the growth/decay factor?
How much will he make in 4 years?
Question 20
3000(1 .12)
:1.12
$4720.56
xy
Growth Factor
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Describe the transformations
g(x) = -4x - 12
Question 21
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Describe the transformations
g(x) = -4x - 12
Question 21
4
12
reflection
stretch by a factor of
shift down units
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Describe the transformations
g(x) = ¼ (3)x-2 + 5
Question 22
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Describe the transformations
g(x) = ¼ (3)x-2 + 5
Question 22
1/ 4shrinkby a factor of
shift right two units
shift up five units
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A manufacturer keeps track of her monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. The function is C(x) = 5,000 + 1.3x.
a. Can any value be in the domain for this function?
b. What is the cost of 2,000 manufactured items?
c. If costs must be kept below $10,000 this month, what is the greatest number of items she can manufacture?
Question 23
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A manufacturer keeps track of her monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. The function is C(x) = 5,000 + 1.3x.
a. Can any value be in the domain for this function?
b. What is the cost of 2,000 manufactured items?
c. If costs must be kept below $10,000 this month, what is the greatest number of items she can manufacture?
Question 23
, ' .
7600
3846
No because you can t have a negative amount ofi tems
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Question 24
2 2 2If 2 4 7, 3 5, ( ) 4
find 2 3 .
f x x x g x x x and h x x
g x f x
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Question 24
24 18 1x x
2 2 2If 2 4 7, 3 5, ( ) 4
find 2 3 .
f x x x g x x x and h x x
g x f x
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Question 25
2 2 2If 2 4 7, 3 5, ( ) 4
find h .
f x x x g x x x and h x x
x f x
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Question 25
4 3 28 16 35x x x
2 2 2If 2 4 7, 3 5, ( ) 4
find h .
f x x x g x x x and h x x
x f x