Exponential Functions
Write an exponential function f(x) based on the following table..
(0, 10), (1, 30)
f(x) = 10(3)x
What's the vertex of...
y = 2(x-4)2 + 6
(4,6)
Is the following function exponential or linear... why?
(0, 8), (1, 20), (2, 50)
The function is exponential because the function represents a pattern of repeated multiplication (x 3.5)
Find the zeroes: 4x2 + 32x - 80 = 0
4 (x + 10) (x - 2)
x = -10 x = 2
How many solutions does the following equation have?
x4 + 3x - 8 = -2x3 + 6x2 - 11
BIGGEST EXPONENT = X4
4 Solutions
In f(x) = 10(3)x, what does the 10 represent? What does the 3 represent?
The 10 represents the starting value.
The 3 represents the growth factor or how much the function is being multiplied by during each interval.
Describe the shift of the vertex of y = (x+2)2 from the origin.
Shift = 2 to the left
Ah-Breanna and Chioma both start out with 10 Pringles. Ah-Breanna triples her pringle count every hour and Chioma adds 50 to her pringle count every hour. Complete the table.
See Table
Given the function for height in feet, h(x) = -2x2 + 12x + 8.
What is the starting height of the function?
8 feet
Find the zeroes of: y = (x2 + 7x + 12)(x - 2)
x = -4 x = -3 x = 2
l(x) = 12(2)x
x = 4
l(4) = 192 leopards
Describe the transformation of y = 3x2 + 2
1. Graph stretches / narrows vertically (k = 3)
2. Graphic shifts vertically 2 units up
How many Pringles does Chioma have after 5 hours? How many Pringles does Ah-Breanna have?
Chioma: 260 Pringles
Ah-Breanna: 2,430 Pringles
Given the function for height in feet, h(x) = -2x2 + 12x + 8.
What is the maximum height of the function?
-b/2a = -12/-4 = 3 = x
y = -2(3)2 + 12(3) + 8 = -18 + 36 + 8 = 26
26 feet
a = 1 b = 8 c = 9
b2 - 4ac = 64 - 36 = 28
28 is positive, so 2 solutions
xWrite an exponential function based on the inventory of books, b(x), if North Star started with 400 books and the amount is depreciating by 4 percent of books each day.
b(x) = 400 (0.96)x
Describe the transformation of f(x) = -3(x-4)2 + 5
2. x3 = stretched/narrowed vertically
3. -4 = Shifts 4 units horizontally to the right
5. + 5 = Shifts 5 units vertically up
Chioma claims both functions can be modeled by a linear equation. Is Chioma correct - why or why not?
Chioma = Linear (Pattern of Addition)
Ah-Breanna = Exponential (Pattern of Multiplication)
Solve for x: 3(x+2)2 = A
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Find the domain and range of y = x2 + 8x + 9
Domain: All Real Numbers (no restrictions on x)
Range: Vertex = Max (a is positive)
-b/2a = -4 y = (-4)2 + 8(-4) + 9
Vertex = (-4, -7)
Maximum = -7
Range: Y is less than or equal to -7
Is this a growth or decay function? Why?
Decay because the b-value (growth factor) is less than 1. Depreciates means decreases or goes down.
Convert to Vertex Form By Completing the Square:
y = x2 + 8x - 3
y = (x + 4)2 - 19
Vertex: (-4, -19)
Given the two points: (0, 12) and (2, 48)...
What is the value of y when x = 4 if the function is EXPONENTIAL?
What is the value of y when x = 4 if the function is LINEAR?
EXPONENTIAL
a = 12 b = 2
y = 12(2)x
x = 4
y = 12(2)4 = 12(16) = 192
EXPONENTIAL: Y = 192
LINEAR : b = 12
m = (48 - 12) / (2-0) = 36/2 = 18
y = mx + b y = 18x + 12
x = 4 y = 18(4) + 12 = 72 + 12 = 84
LINEAR: Y = 84
f(x) = x2 + 3x + 8
Find f(x + 1)
f(x +1) = (x+1)2 + 3(x+1) + 8
= x2 + x + 1 + 3x + 3 + 8
= x2 + 4x + 12
Jayson makes $10/hr working at school and $20 an hour working at a coffee shop. If Jayson wants to work no more than 8 hours and wants to earn at least $115, write a series of inequalities to represent his situation.
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