Which quadratic rule represents the data in the table?
x
–1
0
1
2
3
y
–4
–5
–4
–1
4
A. y = –2x² + 5
B. y = –x² + 5
C. y = x² – 5
D. y = x² + 5
D. y = x² + 5
Which function rule represents the data in the table?
x
–3
–2
–1
0
1
y
–1
2
5
8
11
A. y = –3x – 8
B. y = one-thirdx – 8
C. y = one-thirdx + 8
D. y = 3x + 8
D. y = 3x + 8
A 154-lb person burns 420 calories per hour riding an exercise bicycle at a rate of 15 mi/hr. Write a function rule to represent the total calories burned over time by that person. Explain how the information in the problem relates to the function.
Let's start by identifying the variables involved in this problem. We have:
- x = time spent riding the exercise bicycle (measured in hours)
- y = total calories burned by the person
According to the problem, the person burns 420 calories per hour riding the exercise bicycle at a rate of 15 mi/hr. So we can say that the rate of calories burned (in calories per hour) is constant and equal to 420. We also know that the person is riding at a rate of 15 miles per hour, but we don't need that value to calculate the total calories burned.
To find the function rule, we need to express the total calories burned as a function of the time spent riding. We can do this by multiplying the rate of calories burned by the time spent riding, like this:
y = 420x
This function rule represents the total calories burned over time by the person. It tells us that for each hour spent riding the exercise bicycle, the person burns 420 calories. To find the total calories burned for any amount of time, we simply plug in the value of x (in hours) into the function rule.
In summary, the information in the problem gives us the rate of calories burned (in calories per hour) and the time spent riding (in hours), which we use to calculate the total calories burned. This relationship is expressed by the function rule y = 420x.
Explain how to write a function rule from the table below. Then write a function rule.
x 0 2 4 6
y 2 1 0 –1
To write a function rule from a table, we need to look for a pattern in the x and y values. In other words, we need to figure out how the y values are related to the x values.
Looking at the table, we can see that as x increases by 2, y decreases by 1. Specifically, y starts at 2, then goes to 1, then to 0, then to -1 as x increases by 2 each time. This tells us that the function is decreasing by a constant amount as x increases. We can conclude that the function is linear, and we can use the slope-intercept form of the equation to write the function rule.
The slope-intercept form of a linear equation is: y = mx + b, where m is the slope and b is the y-intercept. We can use the information from the table to find the slope and y-intercept.
First, we can find the slope by calculating the change in y over the change in x. From x = 0 to x = 2, the change in y is -1 - 2 = -3, and the change in x is 2 - 0 = 2. So the slope is -3/2.
Next, we can find the y-intercept by looking at the y value when x = 0. From the table, we see that y = 2 when x = 0. So the y-intercept is 2.
Putting these pieces together, the function rule for this table is:
y = -3/2 x + 2
This function represents a linear relationship between the x and y values in the table. It tells us that for every increase of 2 in x, y decreases by 3/2. The y-intercept of 2 tells us that when x = 0, y is equal to 2.
What are the next three terms in the sequence?
–1, 9, 19, 29, …
A. 38, 37, 32
B. 40, 51, 62
C. 39, 49, 59
D. 38, 47, 56
To find the pattern in this sequence, we should look at the differences between the terms:
1. The difference between the first and second terms is 9 - (-1) = 10.
2. The difference between the second and third terms is 19 - 9 = 10.
3. The difference between the third and fourth terms is 29 - 19 = 10.
Since the differences between the terms are all the same, we can conclude that the sequence is an arithmetic sequence with a common difference of 10.
Using this information, we can find the next three terms in the sequence:
1. To get to the fifth term, we add 10 to the fourth term, which is 29. So the fifth term is 39.
2. To get to the sixth term, we add 10 to the fifth term, which is 39. So the sixth term is 49.
3. To get to the seventh term, we add 10 to the sixth term, which is 49. So the seventh term is 59.
Therefore, the next three terms in the sequence are 39, 49, and 59, which is option C.
Geoff planted dahlias in his garden. Dahlias have bulbs that divide and reproduce underground. In the first year, Geoff’s garden produced 8 bulbs. In the second year, it produced 16 bulbs, and in the third year it produced 32 bulbs. If this pattern continues, how many bulbs should Geoff expect in the sixth year?
A. 64 bulbs
B. 512 bulbs
C. 128 bulbs
D. 256 bulbs