se the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 6 to 6 in increments of 1. An upward slanting line passing through two plotted points is graphed on the plane. The line passes through points plotted at coordinates left parenthesis 0 comma negative 3 right parenthesis, and left parenthesis 3 comma 0 right parenthesis.
The graph of a relation is given. Apply the vertical line test to determine if this relation is a function.
(1 point)
Responses
There is not enough information to determine whether this relation is a function.
There is not enough information to determine whether this relation is a function.
Yes, the given relation is a function.
Yes, the given relation is a function.
No, the given relation is not a function.
No, the given relation is not a function.
The relation is a straight line.
Yes, the given relation is a function. Each input (x-value) corresponds to exactly one output (y-value) along the line passing through the points (0, -3) and (3, 0). The vertical line test confirms that there is only one output for each input, indicating that this relation is a function.
Among the options given, the linear function is:
2y - 5x = 9
This is not currently in slope-intercept form y = mx + b, so we will rearrange it:
2y - 5x = 9
2y = 5x + 9
y = 5/2 x + 9/2
Therefore, the linear function is y = 5/2 x + 9/2.
To determine which point does not belong to the graph of the function y = (x+1)^3 - 2, we can substitute the x and y values of each point into the function and see if the equation is satisfied.
1. For point (-3, 6):
y = (-3+1)^3 - 2
y = (-2)^3 - 2
y = -8 - 2
y = -10
This means that (-3, 6) does not belong to the graph, as the y-coordinate should be -10 instead of 6.
2. For point (0, -1):
y = (0+1)^3 - 2
y = 1^3 - 2
y = 1 - 2
y = -1
This point satisfies the equation, so it belongs to the graph.
3. For point (-3, -10):
y = (-3+1)^3 - 2
y = (-2)^3 - 2
y = -8 - 2
y = -10
This point satisfies the equation, so it belongs to the graph.
4. For point (-2, -3):
y = (-2+1)^3 - 2
y = (-1)^3 - 2
y = -1 - 2
y = -3
This point satisfies the equation, so it belongs to the graph.
Therefore, the point that does not belong to the graph of the function y = (x+1)^3 - 2 is (-3, 6).
According to the given graph of average rainfall by month, the wettest months of the year are November, December, and January. These months have the highest average rainfall, with December having the highest average rainfall of 3.2 inches. So, the correct response is:
November, December, and January
Which of the following is a linear function?(1 point)
Responses
2y−5x=9
2 y minus 5 x equals 9
x2+y=33
x squared plus y equals 33
y=−12x+78, x≠0
y equals negative Start Fraction 12 over x End Fraction plus Start Fraction 7 over 8 End Fraction comma x is not equal to 0
y=2x3+4
The linear function among the given options is:
y = -12x + 78, x ≠ 0
This is a linear function because it is in the form of y = mx + b, where m is the slope and b is the y-intercept.
Which of the following is a linear function?(1 point)
Responses
2y−5x=9
2 y minus 5 x is equal to 9 - no response given
x^2+y=33
x squared plus y is equal to 33 - no response given
y=−12/x+7/8, x≠0
y=−12/x+7/8, x≠0
y=2x^3+4
y is equal to 2 x cubed plus 4 - no response given
Which of the following points does not belong to the graph of the function y=(x+1)^3−2
?(1 point)
Responses
(−3,6)
left parenthesis negative 3 comma 6 right parenthesis
(0,−1)
left parenthesis 0 comma negative 1 right parenthesis
(−3,−10)
left parenthesis negative 3 comma negative 10 right parenthesis
(−2,−3)
According to the given graph, which of the following are the wettest months of the year?
(1 point)
Responses
November, December, and January
November, December, and January
October, November, and December
October, November, and December
January, May, and December
January, May, and December
June, July, and August
June, July, and August