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
When the equation y = 4x - 1 is graphed, it forms a straight line. Upon applying the vertical line test (where a vertical line is drawn through the graph and intersects the graph at only one point), it can be seen that the relation passes the test, indicating that y = 4x - 1 is a function.
Determine if 7x^2 + y = 5 is a linear or nonlinear function.
A. The graph of the function 7x^2 + y = 5 is not a straight line.
B. The function 7x^2 + y = 5 is a nonlinear function.
C. There is not enough information to determine if 7x^2 + y = 5 is a linear or nonlinear function.
D. The function 7x^2 + y = 5 is a linear function.
B. The function 7x^2 + y = 5 is a nonlinear function.
This is because the equation is not in the form of a linear equation (y = mx + b), and when graphed, it does not form a straight line. Instead, it represents a parabolic curve, indicating that it is a nonlinear function.
Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x-axis and y-axis both range from negative 6 to 6 in one-unit increments. A downward slanting line is graphed on the coordinate plane. The line passes through points plotted at left parenthesis 0 comma 3 right parenthesis, and left parenthesis 5 comma 1 right parenthesis.
Determine if the given graph is the graph of the function y = −25x + 3. Enter 1 for yes. Enter 2 for no.
2
The graph found in the illustration does not represent the function y = -25x + 3. The points given in the illustration create a line with a different slope and y-intercept than the function y = -25x + 3. Therefore, enter 2 for no.
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.
The initial value is b = __, and the rate of change is m = __.
The initial value in the context of this problem is the value of the plant's height when the growth started, so it is the height of the plant today which is 10 inches which can also be written as 10/12 feet (since 1 foot = 12 inches).
The rate of change is the rate at which the height of the plant is increasing each day, which is 1.7 inches.
Therefore,
The initial value: b = 10/12 feet, which is equivalent to b = 5/6 feet
The rate of change: 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.
The rate of change is m = __, and the initial value is b = __.
To determine the rate of change and the initial value of the linear function given by the table, we can first calculate the rate of change (slope) using the formula:
m = (y2 - y1) / (x2 - x1)
Taking the points (2, 22) and (8, 25) from the table:
m = (25 - 22) / (8 - 2)
m = 3 / 6
m = 0.5
So, the rate of change (slope) is m = 0.5.
To find the initial value (y-intercept), we can consider one of the points and substitute it into the equation of a line in the form y = mx + b. Let's use the point (2, 22):
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value is b = 21.
So, the rate of change is m = 0.5 and the initial value is b = 21.
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. A downward slanting line is plotted on the coordinate plane. The downward slanting line with arrows on both ends passes through the following closed points: left parenthesis negative 3 comma 4 right parenthesis, left parenthesis 0 comma 3 right parenthesis, left parenthesis 3 comma 2 right parenthesis, and left parenthesis 6 comma 1 right parenthesis.
Determine the initial value and the rate of change of the linear function as given in the graph. Round the answer to three decimal places as needed.
The initial value is __, and the rate of change is __.