Rates of Change
The change in y over the change in x.
What is the slope of a line or what is slope?
the equation of an axis of symmetry that goes through (4,1)
What is x=4?
all x values that will satisfy the equation 3x^2 + 10x + 8 = 0
What are x = -2 and x = -4/3 ?
The logarithm form of 22=5^x
What is log5 22?
the simplified value for f(3) if f(x) = sqrt(4x+8)
What is two times the square root of five?
The rate of change between the points (5, 250) and (15, 300).
What is m=5 or what is 5?
the point - slope formula.
What is (y-y1) = m(x-x1)?
The solution to the inequality 3x - 7 ≤ 38 or -5x + 2 < - 123 (write in interval notation).
What is (-∞, 15] U (25, ∞) ?
The answer to ln(4x - 7) = 3. (round to 2 decimals)
What is x=6.77?
Another word for increasing at a decreasing rate.
What is "concave down"?
A student athlete performs 20 pushups and her heart rate measured 83 bpm then did 48 pushups and her heart rate measured 102 bpm. The average change in heart rate.
What is 0.679?
The transformations performed on y=|x| to get y = - 3|x - 3| +10.
What is shift 3 units right, up 10 units, stretch of 3 units and a reflection over the x-axis?
A value for x that satisfies the equation 4/(x+2) = 103.
What is 8?
A value for x, in its simplest form, that satisfies the equation 4^x = 1/2
What is -1/2 ?
f(g(x)) if f(x) = 4x^2 - 8x + 1 and g(x) = 2x +1.
What is 16x^2 - 3?
A student athlete performs 20 pushups and her heart rate measured 83 bpm then did 48 pushups and her heart rate measured 102 bpm. The linear function H(x) that represents her heart rate after x pushups. (round to 3 decimals)
What is H(x)=0.679x + 69.42?
A new mini-roller coaster at an amusement park has a track shaped by the polynomial:
h(x)= -x^3 + 6x^2 - 8x where
h(x) = height of the car (in feet),
x = time in seconds after the ride starts.
When the roller coaster car is at its highest.
The roller coaster's max height.
What is x=3.15 seconds?
What is 3.08 feet?
Your student council is selling tickets for Sadies. They are selling two types of tickets:
Standard tickets
VIP tickets (come with a snack and a photo pass)
On the first day, they sell 52 tickets in total and make $640. A standard ticket costs $10.
A VIP ticket costs $20.
The number of standard tickets and the number of VIP tickets sold on the first day.
What is 40 standard tickets and 12 VIP tickets?
the solution of the equation of 2 = log(x+4)
What is x = 96?
(fog)(x) if f(x)=sqrt(x) and g(x)=x^2 + 4
What is sqrt(x^2 + 4)? [which is NOT equivalent to x+2]
A manufacturing company produces custom metal rods whose total production cost depends on the length of the rods ordered.
A customer places one order for 40 meters of rod and is charged $620 total.
Another customer places an order for 85 meters of rod and is charged $1,255 total.
The rate of change (slope) of the cost with respect to rod length.
The linear equation C(L) that models the relationship between total cost and rod length.
1. What is m=14.11
2. What is C(x) = 14.11x + 55.56
The asymptotes for f(x) = 3x^2 + 8 / 4x -7.
What is x=7/4?
Jordan wants to save money for a used car.
He deposits $1,500 into a savings account that earns 4.8% annual interest, compounded monthly.
The money Jordan will have in the account after 3 years. (round to cents)
What is $1,731.83?
A scientist is studying the growth of a bacterial culture. The number of bacteria doubles every 4.5 hours. At the start of the experiment, the culture contains 3,200 bacteria.
The population is modeled by:
N(t)=3200⋅2^t/4.5
where t = hours after the start of the experiment and N(t) = number of bacteria
The number of hours after the start of the experiment where the bacteria count first reaches 51,200 bacteria.
What is t=18 hours?
A company models its profit (in thousands of dollars) from producing and selling a new product using the polynomial function
P(x)=−2x^4+5x^3+18x^2−20x+7
where x represents the number of hundreds of units produced.
The local maxima and local minima.
What is x=-1.68, x=3.07 (local max)?
What is x=0.48 (local min)?