1. The ordered pairs (0, 1), (1, 4), (2, 16), (3, 64), and (4, 256) represent a function. What is a rule that represents this function?
y = 4^x
y = 4x
y = x^4
y = x + 4
2. Consider the relationship between the height of a tree and time. Time would be considered which of the following?
function
input function
independent variable
dependent variable
3. Which of the following describes the relationship between the length of a rectangle and its width as width varies and area stays the same?
As width decreases, length stays constant.
As width decreases, length increases.
As width decreases, length decreases.
As width increases, area increases.
My answers:
1. ?
2. independent variable
3. As width decreases, length increases.
1. The rule that represents the given function is y = 4^x.
Explanation: Looking at the ordered pairs, we can observe that the y-value is obtained by raising 4 to the power of the x-value. For example, (1, 4) means that when x = 1, y = 4^1 = 4.
2. The time in the relationship between the height of a tree and time would be considered the independent variable.
Explanation: In this scenario, time is being used to determine the height of the tree. Therefore, the height is dependent on the time, and time is considered the independent variable.
3. The relationship between the length of a rectangle and its width, as the width varies and the area stays the same, is described as follows: As width decreases, length increases.
Explanation: When the width decreases, keeping the area constant, the length must increase in order to compensate for the decrease in width and maintain the same area. Therefore, as the width decreases, the length increases.
1. To find the rule that represents the given function, we need to look for patterns in the ordered pairs. In this case, notice that the y-values are obtained by raising 4 to the power of the x-values. So, the rule that represents this function is y = 4^x.
2. In the context of the relationship between the height of a tree and time, time would be considered as the independent variable. The independent variable is the variable that is manipulated or controlled by the experimenter or input into a function.
3. The correct description of the relationship between the length of a rectangle and its width as the area stays the same is "As width decreases, length increases." This can be explained by the formula for the area of a rectangle, which is length multiplied by width. If the area is constant, decreasing the width would require the length to increase in order to maintain the same area.
well, zero out of three is not that great.
1. did you notice
4^0 = 1
4^1 = 4
4^2 = 16
4^3 = 64 and
4^4 = 256 ??
2. The height of the tree in my backyard "depends" on how long it has been there, so ....
3. suppose we have an area of 20 cm^2 and it stays at 20
if the width = 2 cm, the length would be 10 cm
if we increase the width to 4 cm, the length would be decreased to 5 cm.
suppose we decrease the width from 4 to 3
then the length will be 20/3 which is greater than 5
you said that as width increases, the length increases, but I contradicted that with my example
so what do you think?