MATH SOLVE

9 months ago

Q:
# 1)Why is it impossible for a function to have fewer values in its domain than in its range? Explain how you can tell the function f(x)={x-5} is not linear by using points on its graph.Study the function below.f(x) = –3xLabel the function as proportional or non-proportional.Explain your reasoning.Which of the following equations would not be a line when graphed? Explain how you can tell by just looking at the equations.y=9y=-2x power of 2 +4y= -8x+3y=7/xmake u the brainliest whoever gets it correct 60 points whoever gets it plz put serious answers and not some childidh one ok

Accepted Solution

A:

Part (1):For a relation to be called a function, each input must have one and only one corresponding output.Now, we know that the input of the relation is known as its domain while the output is known as its range.Based on the above definition, each input (value from domain) has only one output (value from range)Therefore, the values for domain and range are equal, otherwise, the relation won't be a function

Part (2):The graph of the function is shown in the attached image.Now, a linear function:1- is a straight line. This means that it has neither curved nor sharped bends.In the graph of the given function, we can see that it has a sharp bend at the point (5,0)2- has a constant slope all over the graph.Let's test this condition on our graph:For the two points (0,5) and (1,4):slope = [tex] \frac{4-5}{1-0} = -1 [/tex]For the two points (6,1) and (7,2):slope = [tex] \frac{2-1}{7-6} = 1 [/tex]We can see that the slope is not constant along the whole graph.Based on the above two conditions, the absolute function is not a linear function

Part(3):There are two types of proportionality:1- Direct proportionality: This means that as one value increases, the other would increase at the same rateLet's check this on the given function:f (x) = -3xAt x = 1 ..........> f (x) = -3(1) = -3At x = 2 .........> f (x) = -3(2) = -6We can note that the condition of direct proportionality is not fulfilled, therefore, the relation is not showing direct proportionality2- Inverse proportionality: This means that as one value increases, the other would decrease by the same rate.Inverse proportionality has the general formula: y = [tex] \frac{k}{x} [/tex]where k is the constant of proportionality.The given function is: f (x) = -3xWe can note that it does not have the same format as the general formula of the inverse proportionality.Therefore, the given relation does not show inverse proportionalityBased on the above, we can conclude that the given relation is non-proportional

Part (4):The graphs are shown in the second attached imageLet's check the givens:1) y = 9We know that this would be a line parallel to the x-axis constant at y = 9Therefore, this choice is correct2) -2x² + 4We know that the second degree polynomial gives a curve not a line.Therefore, this choice is incorrect3) y = -8 + 3The general form of the linear line is y = mx + bThe given equation has the same format as the general one.Therefore, this choice is correct4) y = 7/xAgain, the general form of the linear line is y = mx + bThe given equation has the a different format than the general one.Therefore, this choice is incorrect

Hope this helps :)

Part (2):The graph of the function is shown in the attached image.Now, a linear function:1- is a straight line. This means that it has neither curved nor sharped bends.In the graph of the given function, we can see that it has a sharp bend at the point (5,0)2- has a constant slope all over the graph.Let's test this condition on our graph:For the two points (0,5) and (1,4):slope = [tex] \frac{4-5}{1-0} = -1 [/tex]For the two points (6,1) and (7,2):slope = [tex] \frac{2-1}{7-6} = 1 [/tex]We can see that the slope is not constant along the whole graph.Based on the above two conditions, the absolute function is not a linear function

Part(3):There are two types of proportionality:1- Direct proportionality: This means that as one value increases, the other would increase at the same rateLet's check this on the given function:f (x) = -3xAt x = 1 ..........> f (x) = -3(1) = -3At x = 2 .........> f (x) = -3(2) = -6We can note that the condition of direct proportionality is not fulfilled, therefore, the relation is not showing direct proportionality2- Inverse proportionality: This means that as one value increases, the other would decrease by the same rate.Inverse proportionality has the general formula: y = [tex] \frac{k}{x} [/tex]where k is the constant of proportionality.The given function is: f (x) = -3xWe can note that it does not have the same format as the general formula of the inverse proportionality.Therefore, the given relation does not show inverse proportionalityBased on the above, we can conclude that the given relation is non-proportional

Part (4):The graphs are shown in the second attached imageLet's check the givens:1) y = 9We know that this would be a line parallel to the x-axis constant at y = 9Therefore, this choice is correct2) -2x² + 4We know that the second degree polynomial gives a curve not a line.Therefore, this choice is incorrect3) y = -8 + 3The general form of the linear line is y = mx + bThe given equation has the same format as the general one.Therefore, this choice is correct4) y = 7/xAgain, the general form of the linear line is y = mx + bThe given equation has the a different format than the general one.Therefore, this choice is incorrect

Hope this helps :)