1
For each pair of functions, determine which function y is changing more rapidly:
a
Function 1:
x 0 1 2 3 y 3 10 17 24
Function 2:
x -1 0 1 2 y -1 3 7 11
b
Function 3:
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
Function 4:
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
2
For each pairs of functions, determine which has the greater y-intercept:
a
Function 1:
y = 4 x^2 + 6x+3
Function 2:
y = 4 x + 6
b
Function 3:
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
Function 4:
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
3
The parabola C is given by y = \dfrac{\left(x - 3\right)^{2}}{9} + 7 and the exponential function D is given by y = - 8^{x} + 1.
a
Graph the functions on the same coordinate plane.
b
Determine which function has the lower y-intercept.
4
The parabola E is given by y = 12 \left(x - 1\right)^{2} - 4 and the exponential function F is given by y = 3^{x} + 4.
a
Graph the functions on the same coordinate plane.
b
State which function increases at a faster rate for very large values of x.
5
The population of two different bacteria, labeled J and K, are given by the shown table of values:
Bacteria J:
| t \text{ (Time in days)} | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| P\text{ (Population)} | 1 | 120 | 480 | 1080 | 1920 |
Bacteria K:
| t \text{ (Time in days)} | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Q\text{ (Population)} | 1 | 50 | 2500 | 1.25 \times 10^{5} | 6.25 \times 10^{6} |
a
The population P of bacteria J at time t can be modeled using the general equation P \left( t \right) = at^2, where a \geq 0. By using the table of values, graph P \left( t \right) for t \gt 0.
b
The population Q of bacteria K at time t can be modeled using the general equation Q \left( t \right) = b^{t}, where b \gt 1. By using the table of values, graph Q \left( t \right) for t \gt 0.
c
Determine which population of bacteria is growing faster.
6
For each pair of functions, determine which has the greater y-intercept:
a
Function 1: The line with a slope of 4 that crosses the y-axis at \left(0, 6\right).
Function 2: The parabola given by the equation y = x^2 + 4.
b
Function 3:
x 2 4 6 y 2 -2 -6
Function 4:
-2
-1
1
2
x
1
2
3
4
5
y
c
Function 5:
x 2 4 6 y 19 35 51
Function 6:
y = 4^x + 6
7
Consider each pair of functions:
Function A:
\\y = - 4^x+3
Function B:
-4
-2
2
4
6
8
10
12
x
-4
-2
2
4
6
8
10
12
y
a
Determine how many x-intercept(s) function A has.
b
Determine how many x-intercept(s) function B has.
8
The parabola J is given by y = -9 x^2+20.
The table shows the function values for exponential function K:
| x | -2 | -1 | 1 | 2 | 3 |
|---|---|---|---|---|---|
| y | \dfrac{5}{9} | \dfrac{5}{3} | 15 | 45 | 135 |
a
Determine if the exponential function K is increasing or decreasing.
b
Graph the functions J and K on the same coordinate plane.
c
Determine what transformation we can apply to the function y=3^{x} to produce function K.
9
The line P is given by y = - 4 + \dfrac{4 x}{3} and the parabola Q is given by y = - \left(x - 1\right) \left(x - 4\right).
a
Graph the line P and the parabola Q on the same coordinate plane.
b
Identify how many times P and Q intersect.
c
Identify which function has the higher function value at x = 0.
10
The table of values for the function P and for the function Q are provided.
Function P:
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | 9 | 6 | 3 | 0 | -3 |
Function Q:
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 6 | 3 | 2 | 3 | 6 |
a
Determine what type of functions Function P and Function Q are.
b
Graph the functions on the same coordinate plane.
c
As x gets very large, determine which function will have the greater value.
11
Some friends decide to go camping for the weekend. They cannot all fit in one car so some of them catch a bus to the campground, which is 450 \text{ km} from home. Those in the car started driving at 8:00 AM and arrived at the campground at 3:30 PM, driving at a constant speed. The bus also drives at a constant speed and takes the same route as the car. Its distance in kilometers \left(y\right) from home x hours after leaving is given by the equation y = 71 x.
a
Determine the speed of the car, in kilometers per hour.
b
Determine the speed of the bus, in kilometers per hour.
c
Determine which vehicle was traveling faster.
12
Consider the functions f \left(x\right) = 2x, g \left(x\right) = 2x^2 and h \left(x\right) = 2^x for x \geq 0.
a
Describe the pattern of how each of the functions increases. Explain how you identified the patterns.
b
Compare how the three functions increase as x gets very large.
13
Two companies Crest Corporation and Mint Corporation are operating mines. Crest Corporation’s operations are such that the total amount mined by the nth week is given by the equation C = 10 n^{2}. The total amount mined by Mint Corporation over time is shown in the graph.
5
10
15
20
25
30
35
40
45
50
55
60
\text{Week}
2
4
6
8
10
\text{Amount mined (thousands of metric tons)}
a
If mining operations for both companies were to only last at most a year, determine which company will have mined the most minerals in that time.
b
Determine if the two corporations will ever mine the same amount at the same time after the first week.
c
At the point of intersection, the total quantity of minerals remaining in both mines is equal. If both mining companies continue to operate in the same way indefinitely, determine which company will exhaust their mine first. Explain your reasoning.
14
During a sudden viral outbreak, scientists must decide between two antivirals to try and control the situation. In a laboratory, they apply Adravil and Felicium to two samples of the virus, each containing 200 microbes.
They keep track of the number of microbes in each sample, and notice that the number of microbes using Adravil is increasing by a constant amount of 12 each hour. The table shows the results for Felicium.
| \text{Number of hours }(t) | 0 | 3 | 6 | 9 |
|---|---|---|---|---|
| \text{Number of microbes using Felicium} | 200 | 600 | 1800 | 5400 |
a
Determine which antiviral will better control the number of microbes. Explain your choice.
b
The new antiviral, Tretonin, shows the preliminary results:
| \text{Number of hours }(t) | 0 | 3 | 6 | 9 |
|---|---|---|---|---|
| \text{Number of microbes using Tretonin} | 200 | 202 | 208 | 218 |
If the trends from the first 9 hours continue in the future, determine which treatment will be better of the short-term, and which will be better over the long-term. Justify your answer.
