Transformations
What is the type of translation that describes left or right movement of the function?
Horizontal
Consider a quadratic function with an axis of symmetry x=7. If f(9) = 20 then f(x) = -20 for what other value of x?
5
If 4500(1.04)x represents the amount in a savings account x years after 2017.
1. What is the initial amount in the account?
2. Does the amount after 2017 reflect growth or decay?
1. 4500
2. growth
An oil ship weighs 92 tons empty. It is pumped full of oil at a constant rate of 0.8 tons per minute. Write an equation to represent the weight of the ship. (w=?)
w = 0.8x + 92
If I(p) = 6p - 42 represents the income for selling pizzas, what is a reasonable domain?
x greater than or equal to 0
x >= 0
Describe the transformation of the following function:
(x+4)2 - 3
Left 4
Down 3
b2-4ac represents the discriminant which determines the number of solutions based on its value.If value is
zero you have _______ solutions
positive number you have _______ solutions
negative number you have _______ solutions
one
two
no (will accept zero)
If a car that is purchased for $18000 decreases exponentially by 23%. Write an equation that you would use to calculate the value of the car.
a = 18000 b = 1 - 0.23 = 0.77
y = 18000 (0.77)x
If we know that f(x) = 2x + 3,
find f(x+1).
f(x) = 2(x+1)+3
f(x) = 2x + 2 + 3
f(x) = 2x+5
If f(x) = 8(3)x what is the average rate of change over the interval from 0 to 4?
(0 , 8) (4 , 648)
y2-y1 / x2-x1 = 648-8 / 4-0 = 640/4 = 160
Describe the transformation from
g(x) = x2+2 to f(x) = x2 - 9
down vertically 11
Factor x2 + 11x +30 using any method
(x-method or DESMOS)
(x+6)(x+5)
Consider the function h(x) = 200(0.17)X .
1. What is the y-intercept?
2. What is the constant factor?
3. Does it represent growth or decay?
200
0.17
decay
Write 2x + 3y = 12 in slope-intercept form.
2x+3y=12
3y=-2x+12
3y/3 = -2x/3 + 12/3
y = -2/3 x + 4
y1 = 2x + 6 y2 = x2 + 5x + 6
What would be the solution to y1 = y2 ?
(-3,0) (0,6) or x=-3 y=6
Describe the transformation for the following function:
f(x) = -2(x - 6)2 + 3
Reflection
stretch 2
right 6 horizontally
up 3 vertically
f(x) = 2 and g(x) = x2 - 2x - 13
Find the solution to f(x) = g(x)
x = -3
x = 5
Write an equation for this relationship.
x f(x)
1 12
2 48
3 192
y = (3)(4)x
If f(n) = 20000 + 800n represents the population n years after 2000. What does f(8) = 26400 represent?
Eight years after 2000 (in 2008), the population was 26400.
When completing the square
of x2 - 12x + __ = 5 +__
What value would you square and add to both sides?
36 or (-6)2
Write an absolute value function f(x) to represent the following transformation:
Reflection across x-axis, shrink of 1/2 units, down vertically 4 units, right horizontally 6 units
f(x) = -1/2 |x-6| - 4
f(x) = 2x2 + 4x - 16 Identify the following:
1. x-intercepts 2. y-intercepts
3. vertex 4. axis of symmetry
5. maximum or minimum
1. (-4,0) (2,0) or x=-4 x=2 2. (0,-16)
3. (-1,-18) 4. x = -1
5. minimum
A car is valued at $64800 and it decreases exponentially by 16%. Write a function f(x) to represent these values.
f(x) = 64800(0.84)x
The width of a rectangular deck is 5 less than twice the length. If the perimeter is 68 feet, write an equation that can be used to determine the length.
w = 2L -5 p= 2L + 2W
p = 2L + 2(2L - 5)
p = 6L - 10
Determine if the slope of the following is positive, negative, zero or undefined. (All or nothing)
1. 2x - 4y = -12 2. y = 4 - 3/2x
3. x = 7 4. y = 9
5. horizontal line 6. vertical line
1. positive 2. negative
3. undefined 4. zero
5. zero 6. undefined