To determine if the relation y=4x-1 is a function, we will first graph the relation and then apply the vertical line test.
The graph of the relation y=4x-1 is a straight line with a slope of 4 and a y-intercept of -1. This line passes through all points (x, y) where y=4x-1.
Next, we will apply the vertical line test. The vertical line test states that a relation is a function if every vertical line intersects the graph at most once.
In this case, when we draw vertical lines at different x-values, each vertical line intersects the graph at only one point. Therefore, the relation y=4x-1 passes the vertical line test and is a function.
Therefore, the correct answer is 1. The relation y=4x-1 is a function.
Functions Unit Test 1 of 151 of 15 Items Question Determine if the relation y=4x−1 is a function by first graphing the relation, then applying the vertical line test. Enter 1 if the relation is a function. Enter 2 if the relation is not a function.(1 point)
11 answers
Determine if 7x2+y=5 is a linear or nonlinear function.(1 point) Responses There is not enough information to determine if 7x2+y=5 is a linear or nonlinear function. There is not enough information to determine if 7 x squared plus y equals 5 is a linear or nonlinear function. The function 7x2+y=5 is a nonlinear function. The function 7 x squared plus y equals 5 is a nonlinear function. The function 7x2+y=5 is a linear function. The function 7 x squared plus y equals 5 is a linear function. The graph of the function 7x2+y=5 is not a straight line.
The function 7x^2 + y = 5 is a nonlinear function.
This can be determined because the term 7x^2 in the function indicates a quadratic term, which means that the function is not linear. In a linear function, the highest power of the variable should be 1.
Therefore, the correct response is "The function 7x^2 + y = 5 is a nonlinear function."
This can be determined because the term 7x^2 in the function indicates a quadratic term, which means that the function is not linear. In a linear function, the highest power of the variable should be 1.
Therefore, the correct response is "The function 7x^2 + y = 5 is a nonlinear function."
Use the image to answer the question. Determine if the given graph is the graph of the function y=−25x+3 . Enter 1 for yes. Enter 2 for no. (1 point) Skip to navigation
As an AI language model, I don't have the capability to view or interpret images. Please provide a verbal description of the graph or any specific details related to the function y=-25x+3 so that I can assist you in determining whether the given graph matches the function.
graph the function y=−25x+3 .
I'm unable to create a graph directly in this text-based format. However, I can guide you on how to graph the function y = -25x + 3. Here's how you can do it:
1. **Determine the Slope and Y-Intercept**:
- The slope of the function is -25, which means for every unit increase in x, y decreases by 25 units.
- The y-intercept of the function is 3, which is the point where the function intersects the y-axis.
2. **Plot the Y-Intercept**: Start by plotting the point (0, 3) on the y-axis.
3. **Use the Slope to Find a Second Point**:
- Because the slope is -25, you can use this to find another point on the graph.
- For example, if you move one unit to the right from the y-intercept, you would move down 25 units (due to the negative slope) to get another point.
4. **Draw a Line Through the Points**: Connect the two points you plotted with a straight line.
This process will help you graph the function y = -25x + 3. Once you have the graph, you can then compare it with the given graph to determine if they match.
1. **Determine the Slope and Y-Intercept**:
- The slope of the function is -25, which means for every unit increase in x, y decreases by 25 units.
- The y-intercept of the function is 3, which is the point where the function intersects the y-axis.
2. **Plot the Y-Intercept**: Start by plotting the point (0, 3) on the y-axis.
3. **Use the Slope to Find a Second Point**:
- Because the slope is -25, you can use this to find another point on the graph.
- For example, if you move one unit to the right from the y-intercept, you would move down 25 units (due to the negative slope) to get another point.
4. **Draw a Line Through the Points**: Connect the two points you plotted with a straight line.
This process will help you graph the function y = -25x + 3. Once you have the graph, you can then compare it with the given graph to determine if they match.
Determine the initial value and the rate of change in the following description. Last year, Joshua’s tomato plant reached a maximum height of 2 feet. He is growing another tomato plant this year, and he is tracking its growth. The plant’s height today is 10 inches, and it grows 1.7 inches each day. (1 point)
The initial value is b= , and the rate of change is m= .
The initial value is b= , and the rate of change is m= .
To determine the initial value and rate of change based on the provided description, we can use the information given:
1. Initial value (b): The initial value represents the starting point or the value when the growth began. In this case, when Joshua's tomato plant reached its maximum height last year, it was 2 feet. To convert this to inches (since the current height is mentioned in inches), 2 feet is equal to 24 inches (1 foot = 12 inches). Therefore, the initial value is b = 24 inches.
2. Rate of change (m): The rate of change in this context represents how much the plant's height increases each day. The description states that the plant grows 1.7 inches each day. Therefore, the rate of change is m = 1.7 inches/day.
Therefore, based on the given information:
- The initial value is b = 24 inches.
- The rate of change is m = 1.7 inches/day.
1. Initial value (b): The initial value represents the starting point or the value when the growth began. In this case, when Joshua's tomato plant reached its maximum height last year, it was 2 feet. To convert this to inches (since the current height is mentioned in inches), 2 feet is equal to 24 inches (1 foot = 12 inches). Therefore, the initial value is b = 24 inches.
2. Rate of change (m): The rate of change in this context represents how much the plant's height increases each day. The description states that the plant grows 1.7 inches each day. Therefore, the rate of change is m = 1.7 inches/day.
Therefore, based on the given information:
- The initial value is b = 24 inches.
- The rate of change is m = 1.7 inches/day.
Use the table to answer the question. x y 2 22 8 25 Determine the rate of change and the initial value of the linear function given here as a table of values. (1 point)
The rate of change is m= , and the initial value is b= .
The rate of change is m= , and the initial value is b= .
To find the rate of change (m) and the initial value (b) of the linear function represented by the table of values given, we can use the formula for the slope (rate of change) of a linear function:
Slope (rate of change) = (change in y) / (change in x)
Given the table:
- When x = 2, y = 22
- When x = 8, y = 25
Calculate the change in y:
Change in y = 25 - 22 = 3
Calculate the change in x:
Change in x = 8 - 2 = 6
Now, calculate the rate of change (m):
m = (change in y) / (change in x) = 3 / 6 = 0.5
The rate of change is m = 0.5.
Next, to determine the initial value (b), we can pick one of the points (2, 22) or (8, 25) and use the formula of the linear function:
y = mx + b
Using (2, 22):
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value is b = 21.
In summary:
- The rate of change is m = 0.5
- The initial value is b = 21
Slope (rate of change) = (change in y) / (change in x)
Given the table:
- When x = 2, y = 22
- When x = 8, y = 25
Calculate the change in y:
Change in y = 25 - 22 = 3
Calculate the change in x:
Change in x = 8 - 2 = 6
Now, calculate the rate of change (m):
m = (change in y) / (change in x) = 3 / 6 = 0.5
The rate of change is m = 0.5.
Next, to determine the initial value (b), we can pick one of the points (2, 22) or (8, 25) and use the formula of the linear function:
y = mx + b
Using (2, 22):
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value is b = 21.
In summary:
- The rate of change is m = 0.5
- The initial value is b = 21