1.1-1.2
1.3-1.4
1.5-1.6
1.7
idk
100

f(x) = 2x - 2

g(x) = 7 - x2


Find f(-3) + g(2)

f(-3) = 2(-3) - 2 = -6 - 2 = -8

g(2) = 7 - (2)2 = 7 - 4 = 3


-8 + 3 = -5


100

solve the absolute value equation:

| x + 4 | = 18

x + 4 = 18            -(x + 4) = 18

x + 4 = 18            x + 4 = -18

x = 14                  x = -22

100

Find the inverse of the following equation:

f(x) = x / x + 5

f(x) = x / x + 5

y = x / x + 5

switch x and y

x = y / y + 5

x * (y + 5) = y

xy + 5x = y

5x = y - xy

5x = y(1 - x)

5x / 1 - x = y


f-1(x) = 5x / 1 - x


100

Find the rate of change:

f(x) = 4x2 - 7 on [1, b]

f(b) - f(1) / b - 1

f(b) = 4b2 - 7

f(1) = 4(1)2 - 7 = -3

4b2 - 7 - (-3) / b - 1

4b2 - 4 / b - 1

4(b2 - 1) / b - 1

4(b + 1)(b - 1) / b - 1

= 4(b + 1)

100
Which method determines if a graph is a function

Vertical Line Test

200

Find the Domain and Range of the graph below

Domain: (-3, 1]

Range: [-4, 0]

200

f(x) = x2 + 6x

g(x) = 2 - x

Find f(g(2))

g(2) = 2 - 22 = 2 - 4 = -2

f(-2) = (-2)2 + 6(-2) 

        = 4 - 12 = -8

200

Describe the transformation of this function:

f(x) = 4 * |x - 2| - 6

shift right 2 units

shift down 6 units

vertically stretched by a factor of 4

200

Find the average rate of change of the function f(x)=6−3x2   on   [−2,3]

f(b)−f(a) / b−a 

f(3) - f(-2) / 3 - -2

f(3) = 6 - 3(3)2 = 6 - 27 = -21

f(-2) = 6 - 3(-2)2 = 6 - 12 = -6


-21 - -6 / 3 - -2

-15 / 5 = -3

200

BONUS QUESTION:

A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t)=10√t+5, find the area of the ripple as a function of time

Area of a circle: A = pi * r2

radius: r(t)=10√(t+5)

A = pi * (10√t+5)2

A = pi * 100(t + 5)

300

What is the domain of the following:

f(x) = x2 + 2x + 1

All Real Numbers
300

If h(x) = f(g(x)) and h(x) = (x - 5)3

find f(x) and g(x)

g(x) = x - 5

f(x) = x3


f(g(x)) = f(x - 5) = (x - 5)3​​​​
300

given a function f(x) = x. Transform it to g(x) given the following:

horizontally compressed by 1/2

3 units to the left

shift up 1 unit


g(x) = 2(x + 3) + 1

300

Find the absolute max and/or min

absolute max: 1 at x = -1, 1

absolute min: DNE

300

At the start of a trip, the odometer on a car read 21465. At the end of the trip, 13.5 hours later, the odometer read 22205. Assuming the scale on the odometer is in miles, what is the average speed the car traveled during the trip? Round to the nearest tenth of a mile.

x2−x1 / y2−y1

= 22205−21465 / 13.5−0

≈54.8 miles per hour

400

The quality of gasoline that a station sells in a day is a function of the price. Let Q = f(P) represent the number of gallons of gasoline the station sells in a day if it charges P dollars per gallon. 

Interpret f(3.09) = 7840

When the station sells gasoline for $3.09, they will sell 7840 gallons in a day

400

f(x) = x2 + 6x

g(x) = 2 - x

Find f(g(x))

f(g(x)) = f(2 - x2) = (2 - x2)2 + 6(2 - x2)

= 4 - 4x2 + x4 + 12 - 6x2

= x4 - 10x2 + 16

400

f(x)=2−x 

find f-1(x)

f(x)=2−x     Substitute y for f(x).  

y=2−x     Interchange the variables x and y.  

x=2−y     Solve for y.  

y=2−x     Substitute f-1(x) in for y.  

f-1(x)=2−x  

400

Find the interval of concave up, concave down, and the inflection point

(−∞,0), the function is concave down, while on the interval (0,∞), the function is concave up 

inflection point: (0,1)

400

The price P charged by a taxi company for a trip x miles long is given by the formula

P = f(x) = 3.50 + 2.75x

The company will NOT make any trip longer than 50 miles.

Find the domain and range of this function

Domain: [0, 50] because the company will not go over 50 miles

Range: [3.50, 141]

P = 3.50 + 2.75(50) = 141


500

Find the domain of this function:


8 / sqrt(x + 4)

x + 4 >= 0      (>= means greater than or equal to)

x >= -4

500
Solve the inequality 


- | 1/3x - 3 | >= 17   

(>= means greater than or equal to)


No Solution

Remember: The absolute value of a number n is written as | n | and | n | >= 0


- | 1/3x - 3 | >= 17

| 1/3x - 3 | <= -17

500

Describe the transformation given the following function:

f(x) = -(x + 2)2 - 1

reflected across the x-axis

left 2 units

down 1 unit

500

Let f(x)=1 / x. Find the number c such that the average rate of change of the function f on the interval (1,c) is −1/9

(1/c−1/1) / (c−1)= −1/9   Multiply both sides by (c−1) and 9. 


9 * (1/c - 1) = 1 - c

9/c - 9 = 1 - c   Multiply both sides by c. 

9 - 9c = c - c2

c2 - 10c + 9 = 0     Factor

(c - 9)(c - 1) = 0

c = 1, c = 9

Since 1 is included in the interval, c = 9


500

M
e
n
u