State whether each of the following graphs represents a linear or non-linear relationship:
State whether each of the following equations represents a linear of non-linear relationship.
y=2x
y=x^2
y=5
y=3^x
Complete each of the following tables so that they could represent a linear function:
| Input | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Output | 8 | 12 | 20 | 24 |
| Input | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Output | -8 | -20 | -24 |
| Input | 5 | 10 | 15 | 20 | 25 |
|---|---|---|---|---|---|
| Output | -13 | -73 |
Determine whether the following tables represent a linear relation, a quadratic relation, or neither.
| x | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| y | -4 | -2 | 0 | 2 | 4 | 6 |
| x | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| y | -6 | -3 | 0 | 3 | 0 | -3 |
| x | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| y | 1 | 7 | 17 | 31 | 49 | 71 |
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | -8 | -7 | -5 | -3 | 1 |
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | 5 | 2 | -1 | -4 | -7 |
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | -13 | -6 | -5 | -4 | 3 |
Determine whether the following statements are always, sometimes, or never true. Explain your answer.
Consider the given table of values:
| Time period | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Revenue | -4 | 3 | 10 | 17 | 24 |
Determine if the revenue is changing at a constant rate with respect to the time period.
State if the relationship between time and revenue is linear
The growth of a potted plant over a week is recorded in the table below, with measurements being taken at the end of each day.
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Height (inches) | 1 | 3 | 5 | 7 | 9 | 11 | 13 |
Determine if the growth of the potted plant can be represented by a linear function.
The following table shows the decay rate of 1000 grams of radioactive element D:
| Day | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Mass of D (grams) | 1000 | 500 | 250 | 125 | 62.5 |
Determine if the decay can be modeled by a linear function, quadratic function or neither.
The total volume of water that has dripped from a tap is measured each minute and displayed in the table.
| Time (minutes) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Volume (mL) | 5 | 10 | 15 | 20 | 25 |
State the rule that relates the time and volume.
Determine if the rate of change of the volume is constant with respect to time.
Copy and complete the table.
The total distance traveled by a cyclist is measured each hour and displayed in the table.
| Time (hours) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Distance (miles) | 9 | 18 | 27 | 36 | 45 |
State the rule that relates the time and distance.
Copy and complete the table.
Determine the distance the cyclist would be able to travel in 15 hours.
Scarlett records the number of push ups she does each day and records them in the table.
| Time (days) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Push ups | 18 | 23 | 28 | 33 | 38 |
State the rule that relates the time and push ups.
Copy and complete the table.
Determine how many push ups Scarlett will be doing on the 20th day.
Eileen saves some money each week and deposits it into her savings account. The weekly balance of this account at the end of each week is displayed in the table.
| Time (weeks) | 2 | 3 | 4 | 5 | 6 | 10 | 20 | 50 |
|---|---|---|---|---|---|---|---|---|
| Balance (dollars) | 425 | 450 | 475 | 500 | 525 |
State the rule that relates the time and balance.
Copy and complete the table.
Determine the balance be at the start of the first week.
The cumulative rainfall over a series of 4 days is represented on the graph.
Describe the relationship between time and volume.
Determine if points on the graph lie on a straight line.
The total number of matchbox cars owned by Sally over a series of years is represented on the graph.
Describe the relationship between time and the total number of matchbox cars.
Determine if the points on the graph lie on a straight line.
John is handing out flyers on the street to passersby. The total number of flyers John has handed out is recorded each hour and displayed on the graph.
Describe the relationship between time and the total number of flyers.
Determine if points on the graph lie on a straight line.
If the pattern continues over the next few hours, determine what the total number of flyers will be after six hours.
State whether the function that would be used to model each scenario is linear or non-linear.
Water drops from a leaking tap are falling into a bucket at a constant rate. It has to model the volume of water in the bucket as time passes.
A snowball rolling down a mountain doubles its volume every five seconds. It has to model the volume of the snowball as time passes.
A raindrop falling from the sky speeds up by 9.8 m/s every second as it is pulled down by gravity. It has to model the distance travelled by the raindrop as time passes.
The perimeters and areas for a sequence of similar triangles are shown in the following table:
| Triangle | Perimeter | Area |
|---|---|---|
| 1 | 18 | 30 |
| 2 | 27 | 67.5 |
| 3 | 36 | 120 |
| 4 | 45 | 187.5 |
Draw a graph of the perimeter and area functions.
State whether each function is linear or non-linear.
An amount of \$1000 is invested into two different accounts for a fixed period of time, with account C earning compound interest and account S earning simple interest. The balance of each account over time is shown in the following graph:
State the domain of each function.
Describe how each function increases over the part of the graph that is shown.
State whether each function is linear or non-linear.