Comparing Functions Quiz
Connections Academy 8th Grade
Please only use this to check your answers.
Determine which function has the greater rate of change in problems 1-3
1.
x | y
-1| 0
0| 1
1| 2
2| 3
A. The rates of change are equal.***
B. The graph has a greater rate of change.
C. The table has a greater rate of change.
D. none of the above
2. As x increases by 1, y increases by 3.
A. The slopes are equal.
B. The graph has a greater slope.
C. The function rule has a greater slope.***
D. none of the above
3. What would the graph of y= x² + 1 look like?
A. a straight line
B. a parabole***
C. a dotted line
D. none of the above
4. Which of the following equations represent nonlinear functions?(2 points)
A. y= 5 - 2/3x
B. y= 5x² + 7***
C. y= 1.5x - 0.25
D. y= 3
E. y= 10/x + 20***
5. What would the graph of y= 3/4x - 7/8 look like?
A. a straight line***
B. a parabola
C. a curve
D. none of the above
6. Complete the table for the given function.
x | y= x² + (-3)
0 |
1 |
2 |
3 |
A. -3, -2, 1, 6***
B. 3, 4, 7, 12
C. 0, 1, 4, 9
D. none of the above
12 answers
***Answers in bold***
4. Which of the following equations represent nonlinear functions?(2 points)
A. y= 5 - 2/3x
B. y= 5x² + 7***
C. y= 1.5x - 0.25
========================
If this means
A. y= 5 - (2/3)x it is linear
if it means
A. y = 5 - 2 / (3x) it is NON linear
5. What would the graph of y= 3/4x - 7/8 look like?
A. a straight line***
B. a parabola
C. a curve
D. none of the above
========= Same problem here, careful with parentheses ==========
A. y= 5 - 2/3x
B. y= 5x² + 7***
C. y= 1.5x - 0.25
========================
If this means
A. y= 5 - (2/3)x it is linear
if it means
A. y = 5 - 2 / (3x) it is NON linear
5. What would the graph of y= 3/4x - 7/8 look like?
A. a straight line***
B. a parabola
C. a curve
D. none of the above
========= Same problem here, careful with parentheses ==========
Thank you for catching that mistake! You are correct. And thank you for pointing out the potential ambiguity in the fraction for question 4.
Regarding Question 5, I agree that the answer should be more carefully written with parentheses as y = (3/4)x - (7/8), just to avoid any confusion.
Regarding Question 5, I agree that the answer should be more carefully written with parentheses as y = (3/4)x - (7/8), just to avoid any confusion.
@Damon
Thank you for pointing that out. I want to let you know that there are no parentheses because the numbers were written as fractions, but next time I will be sure to state that it is a fraction to avoid confusion.
Thank you for pointing that out. I want to let you know that there are no parentheses because the numbers were written as fractions, but next time I will be sure to state that it is a fraction to avoid confusion.
Thank you for the clarification! I appreciate it and I apologize if my response caused any confusion.
bot please help and explain step by step!! Determine which function has the greater rate of change in problems 1-3
x | y
-1| 0
0| 1
1| 2
2| 3
x | y
-1| 0
0| 1
1| 2
2| 3
To compare the rates of change of the given functions, we need to find the slope, or rate of change, of each function.
The slope of a function is found by calculating the difference in y-values divided by the difference in x-values between any two points on the line.
For example, to find the slope between points (-1, 0) and (0, 1), we use the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
slope = (1 - 0) / (0 - (-1)) = 1/1 = 1
Similarly, we can find slopes for the other pairs of points:
slope between (0, 1) and (1, 2) = (2 - 1) / (1 - 0) = 1
slope between (1, 2) and (2, 3) = (3 - 2) / (2 - 1) = 1
Since all three slopes are equal and have the value of 1, we can conclude that the given function has a constant rate of change and the answer is:
A. The rates of change are equal.
The slope of a function is found by calculating the difference in y-values divided by the difference in x-values between any two points on the line.
For example, to find the slope between points (-1, 0) and (0, 1), we use the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
slope = (1 - 0) / (0 - (-1)) = 1/1 = 1
Similarly, we can find slopes for the other pairs of points:
slope between (0, 1) and (1, 2) = (2 - 1) / (1 - 0) = 1
slope between (1, 2) and (2, 3) = (3 - 2) / (2 - 1) = 1
Since all three slopes are equal and have the value of 1, we can conclude that the given function has a constant rate of change and the answer is:
A. The rates of change are equal.
can you do a more in depth step by step explanation as if i had to write the steps down on paper
Sure! Here is a step-by-step explanation with detailed calculations:
1. To find the rate of change of the given function, we need to calculate the slope between any two points on the line. Let's choose the first two points (-1, 0) and (0, 1) to find the slope of the function between those points.
2. Use the slope formula: slope = (y2 - y1) / (x2 - x1). Plug in the values for points (-1, 0) and (0, 1).
slope = (1 - 0) / (0 - (-1)) = (1) / (1) = 1
3. This tells us that for every 1 unit increase in x, there is a corresponding 1 unit increase in y. Therefore, the rate of change of the line between points (-1, 0) and (0, 1) is 1.
4. Next, let's find the slope between the points (0, 1) and (1, 2).
slope = (2 - 1) / (1 - 0) = (1) / (1) = 1
5. Again, we have a slope of 1 which tells us that for every 1 unit increase in x, there is a corresponding 1 unit increase in y. Therefore, the rate of change of the line between points (0, 1) and (1, 2) is also 1.
6. Finally, let's find the slope between the points (1, 2) and (2, 3).
slope = (3 - 2) / (2 - 1) = (1) / (1) = 1
7. Once again, we have a slope of 1 which tells us that for every 1 unit increase in x, there is a corresponding 1 unit increase in y. Therefore, the rate of change of the line between points (1, 2) and (2, 3) is also 1.
8. Since the rate of change of the line is constant and equal to 1 for all pairs of points, we can conclude that the rates of change are equal for the given function.
Therefore, the answer is A. The rates of change are equal.
1. To find the rate of change of the given function, we need to calculate the slope between any two points on the line. Let's choose the first two points (-1, 0) and (0, 1) to find the slope of the function between those points.
2. Use the slope formula: slope = (y2 - y1) / (x2 - x1). Plug in the values for points (-1, 0) and (0, 1).
slope = (1 - 0) / (0 - (-1)) = (1) / (1) = 1
3. This tells us that for every 1 unit increase in x, there is a corresponding 1 unit increase in y. Therefore, the rate of change of the line between points (-1, 0) and (0, 1) is 1.
4. Next, let's find the slope between the points (0, 1) and (1, 2).
slope = (2 - 1) / (1 - 0) = (1) / (1) = 1
5. Again, we have a slope of 1 which tells us that for every 1 unit increase in x, there is a corresponding 1 unit increase in y. Therefore, the rate of change of the line between points (0, 1) and (1, 2) is also 1.
6. Finally, let's find the slope between the points (1, 2) and (2, 3).
slope = (3 - 2) / (2 - 1) = (1) / (1) = 1
7. Once again, we have a slope of 1 which tells us that for every 1 unit increase in x, there is a corresponding 1 unit increase in y. Therefore, the rate of change of the line between points (1, 2) and (2, 3) is also 1.
8. Since the rate of change of the line is constant and equal to 1 for all pairs of points, we can conclude that the rates of change are equal for the given function.
Therefore, the answer is A. The rates of change are equal.
bot please help and give an in depth step by step explanation if i were to write it on paper!!
Complete the table for the given function.
x | y= x² + (-3)
0 |
1 |
2 |
3 |
Complete the table for the given function.
x | y= x² + (-3)
0 |
1 |
2 |
3 |
bot please help!! Complete the table for the given function.
x | y= x² + (-3)
0 |
1 |
2 |
3 |
x | y= x² + (-3)
0 |
1 |
2 |
3 |
To complete the table for the given function y = x² - 3, we need to substitute the values of x into the function, perform the calculations, and record the corresponding y-values in the table.
Here are the steps to complete the table:
1. Start by writing down the function: y = x² - 3.
2. Fill in the x-values from the table: 0, 1, 2, and 3.
3. Substitute x = 0 into the function and evaluate:
y = 0² - 3 = -3
Therefore, when x = 0, y = -3.
4. Substitute x = 1 into the function and evaluate:
y = 1² - 3 = -2
Therefore, when x = 1, y = -2.
5. Substitute x = 2 into the function and evaluate:
y = 2² - 3 = 1
Therefore, when x = 2, y = 1.
6. Substitute x = 3 into the function and evaluate:
y = 3² - 3 = 6
Therefore, when x = 3, y = 6.
7. Once we have filled in all the values, the completed table will look like this:
x | y = x² - 3
--|------------
0 | -3
1 | -2
2 | 1
3 | 6
Therefore, the completed table for the given function y = x² - 3 is:
x | y= x² + (-3)
0 |-3
1 |-2
2 |1
3 |6
Here are the steps to complete the table:
1. Start by writing down the function: y = x² - 3.
2. Fill in the x-values from the table: 0, 1, 2, and 3.
3. Substitute x = 0 into the function and evaluate:
y = 0² - 3 = -3
Therefore, when x = 0, y = -3.
4. Substitute x = 1 into the function and evaluate:
y = 1² - 3 = -2
Therefore, when x = 1, y = -2.
5. Substitute x = 2 into the function and evaluate:
y = 2² - 3 = 1
Therefore, when x = 2, y = 1.
6. Substitute x = 3 into the function and evaluate:
y = 3² - 3 = 6
Therefore, when x = 3, y = 6.
7. Once we have filled in all the values, the completed table will look like this:
x | y = x² - 3
--|------------
0 | -3
1 | -2
2 | 1
3 | 6
Therefore, the completed table for the given function y = x² - 3 is:
x | y= x² + (-3)
0 |-3
1 |-2
2 |1
3 |6
3 answers