Functions
Quadratic Functions
Exponential Functions
Comparing Functions
100
Which is the following is a function?
b, c, d
100
What is the y-intercept of the following function?
f(x)=x^2+14x-14
y=-14
(0,-14)
100
Determine whether an equation models growth or decay.
a) growth b) decay
c) growth d) growth
100
Identify the graphs as linear, exponential, quadratic, or neither
Quadratic
Neither
Exponential
200
Given the function
g(m)=\sqrt(m-4)\text{, solve }g(m)=2.
m=8
200
Solve the following quadratic equation. (x - 7)(x + 2) = 0
x = 7 x = -2
200
A population of bacteria doubles every hour. If the culture started with 10 bacteria, write an equation to model the bacteria's the population as a function of time.
y=10(2)^t
200
Identify the following as linear, exponential, quadratic, or neither
7. exp.
8. linear
10. quadratic
11. exp.
300
Miranda cuts grass (g) for $20 an hour and trims hedges (h) for $25 an hour. She is trying to make enough money during the summer to buy a car for $4200. Which inequality represents the number of hours Miranda needs to cut grass and trim hedges?
A.
25g + 20h >= 4200
B.
25g + 20h <= 4200
C.
20g + 25h <= 4200
D.
20g + 24h >= 4200
D.
300
When does this function reach its minimum?
f(x)=x^2-6x+17
(3,8)
300
Given f(x)=4x , find the y-intercept and the growth factor.
y-intercept: (0,1)
growth factor: 4
300
Identify the following as linear, exponential, quadratic, or neither. Explain why
Quadratic. The y values have a second common difference of 2.
400
A. 450 = m + n
B. 450 = mn
C. 450m = n
D. 450 + m= n
B
400
The vertex form for the quadratic function y=x2 - 4x + 8 is ______.
What is (x-2)2+4 ?
400
Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour, how many bacteria will we have by the end of one day?
y=224
y=16,777,216
400
Identify the following as linear, exponential, quadratic, or neither. State your reasoning
Neither, does not have a common difference, second common difference, or common ratio.
500
The sequence shows the total number of days Breanna used her gym membership at the the end of months 1,2,3, and 4
8, 13, 18, 23, ...
Assuming the pattern continues, which function could be used to find the total number of days Breanna used her gym membership at the end of month n?
A. f(n) = n5
B. f(n) = n + 5
C. f(n) = 5n + 3
D. f(n) = 5n - 3
C.
500
The path of a rocket is given by the following function, where 'h' is the height in meters and 't' is the time in seconds.
h(t)=—3t^2 + 30t + 73
a) At what time does the rocket reach its maximum height?
b) What is the maximum height of the rocket?
c) When does the rocket hit the ground (rounded to the nearest second)?
a) 5 seconds
b) 148 m
c) 12 seconds
500
A sample of 1,000 bacteria becomes infected with a virus. Each day, one-fourth of the bacteria sample dies due to the virus. A biologist studying the bacteria models the population of the bacteria with the function P(t) = 1,000(0.75)t, where t is the time, in days.
What is the range of this function in this context?
Any whole number such that 0 < P(t) ≤ 1,000
500
Identify the following as linear, exponential, quadratic, or neither. Explain why.
Exponential. There is a common ratio of 3
600
Find the points of intersection of
y = —4x^2 + 4x + 35
and the line with the equation
y=5x+30.
600
Wheeley Fast Co. makes custom skateboards. Their profit is modeled by y = -2x2 + 14x - 20, where y represents their profit in hundreds of thousands of dollars and x is the number of skateboards they produce in thousands.
When do they break even (y = 0)?
How many skateboards maximize their profits?
Break even @ 5 or 2 thousand skateboards
3.5 thousand skateboards (3500) maximize their profits at $4.5 hundred thousand ($450,000)
600
What is the general equation of exponential growth model? Identity each variable and their meanings. (Hint: the general equation for linear equation is y=mx+b, and state what m and b represents)
y=a(1+r)t , a is the initial value or y-intercept, r is the growth rate, t is the time interval.
600
D