Answer:
If the gift card is $30 the remaining change is 3 dollars
The vertex is (-4,-3)
The axis of symmetry is x=-4
and the transformations are:
To measure George's rate of change, we first set out two pairs of independent and dependent data which in this case is the day number and the point
Independent Data: Day 2 Independent Data: Day 4
Dependent Data: 8 points Dependant Data: 12 points
Then we find the difference between the two independent values and the two dependent values
4 - 2 = 2
12 - 8 =4
To find the rate we use the following formula
the difference of dependent value ÷ the difference of independent value =
4 ÷ 2 = 2
Hence the average rate of change is an increase of 2 points a day
Answer:
d) The limit does not exist
General Formulas and Concepts:
<u>Calculus</u>
Limits
- Right-Side Limit:

- Left-Side Limit:

Limit Rule [Variable Direct Substitution]: 
Limit Property [Addition/Subtraction]: ![\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20%5Bf%28x%29%20%5Cpm%20g%28x%29%5D%20%3D%20%20%5Clim_%7Bx%20%5Cto%20c%7D%20f%28x%29%20%5Cpm%20%5Clim_%7Bx%20%5Cto%20c%7D%20g%28x%29)
Step-by-step explanation:
*Note:
In order for a limit to exist, the right-side and left-side limits must equal each other.
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Find Right-Side Limit</u>
- Substitute in function [Limit]:

- Evaluate limit [Limit Rule - Variable Direct Substitution]:

<u>Step 3: Find Left-Side Limit</u>
- Substitute in function [Limit]:

- Evaluate limit [Limit Rule - Variable Direct Substitution]:

∴ Since
, then 
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
16.2 miles.
Since she paid a $5 tip, the cost for her fare was $23.50. Let x be the number of 0.2-mile increments in the trip:
23.50 = 2.50 + 1 + 0.25(x-1)
This equation comes from the 2.50 home pick-up fee; $1 for the first 0.2-mile increment; and 0.25 for each other 0.2-mile increment.
Using the distributive property, we have:
23.50 = 2.50 + 1 + 0.25*x - 0.25*1
23.50 = 2.50 + 1 + 0.25x - 0.25
Combining like terms,
23.50 = 0.25x + 2.75
Subtracting 2.75 from both sides, we have:
23.50 - 2.75 = 0.25x + 2.75 - 2.75
20.25 = 0.25x
Dividing both sides by 0.25, we have:
20.25/0.25 = 0.25x/0.25
81 = x
This means there are 81 0.2-mile increments in her trip. 81(0.2) = 16.2 miles