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)
To graph the relation, we can plot several points:
When x = 0, y = 4(0) - 1 = -1. So one point is (0, -1).
When x = 1, y = 4(1) - 1 = 3. So another point is (1, 3).
When x = -1, y = 4(-1) - 1 = -5. So another point is (-1, -5).
Plotting these points on a graph, we can see that they lie on a straight line.
[Graph image not available]
Now, let's apply the vertical line test. This test is used to determine if a relation is a function.
If every vertical line intersects the graph at only one point, then the relation is a function.
From the graph, it is clear that every vertical line crosses the graph at a unique point. Therefore, the relation y = 4x - 1 is a function.
So the answer is 1.
Determine if 7x2+y=5 is a linear or nonlinear function.(1 point)
Responses
The graph of the function 7x2+y=5 is not a straight line.
The graph of the function 7 x squared plus y equals 5 is not a straight line.
The function 7x2+y=5 is a nonlinear function.
The function 7 x squared plus y equals 5 is a nonlinear function.
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 linear function.
The function 7x^2 + y = 5 is a nonlinear function because it is not a linear equation.
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 in this case is the height of the tomato plant when it was first planted. In the given description, it states that the plant's height today is 10 inches. Therefore, the initial value, b, is 10 inches.
The rate of change is the amount the plant's height increases each day. In the given description, it states that the plant grows 1.7 inches each day. Therefore, the rate of change, m, is 1.7 inches per day.
So, the initial value is b=10, and the rate of change is m=1.7.
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=
.
To determine the rate of change, we need to find the difference in y-values for each pair of (x, y) values in the table.
For the first pair (2, 22) and the second pair (8, 25), the change in y is 25 - 22 = 3.
Now, we can calculate the rate of change by dividing the change in y by the change in x.
For the given table, the change in x is 8 - 2 = 6.
So, the rate of change, m, is 3/6 = 0.5.
To determine the initial value, we can look at the y-value when x = 0. However, there is no information given for x = 0 in the table. Therefore, we can't determine the initial value, b, using the given table.
So, the rate of change is m = 0.5 and the initial value is not able to be determined.
Manuel got a new job and was given a hiring bonus along with his monthly salary. His earnings after x months are modeled by the function f(x)=1,500x+300 . How much did he receive as a hiring bonus?(1 point)
The equation y=mx+b defines what type of function?(1 point)
Responses
an initial value function
an initial value function
a slope function
a slope function
a nonlinear function
a nonlinear function
a linear function
Use the table to answer the question.
x y
6 16
15 43
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.
(1 point)