9. Let y=3x+2 a) typically we write points in this scenario as (x,y), not (y,x), why is that? b) on a horizontal axis, represent 3 things: x=-2, x=4, and Δx=4-(-2). c) on a vertical axis, represent 3 things: y=-4, y=14, and Δy=14-(-4). d) draw a sketch of y=f(x) which includes the points (-2,-4) and (4,14). Mark and label Δx and Δy for those two points on this graph. e) calculate that rate, then write the change equation for x and y f) if the change in x is 2, what is the change in y? g) if the change in y is -12, what is the change in x? h) if we swapped x and y (with x on the vertical axis so x=g(y)), what would the rate be?

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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9. Let y=3x+2

a) typically we write points in this scenario as (x,y), not (y,x), why is that?

b) on a horizontal axis, represent 3 things: x=-2, x=4, and Δx=4-(-2).

c) on a vertical axis, represent 3 things: y=-4, y=14, and Δy=14-(-4).

d) draw a sketch of y=f(x) which includes the points (-2,-4) and (4,14). Mark and label Δx and Δy for those two points on this graph.

e) calculate that rate, then write the change equation for x and y

f) if the change in x is 2, what is the change in y?

g) if the change in y is -12, what is the change in x?

h) if we swapped x and y (with x on the vertical axis so x=g(y)), what would the rate be?

Expert Solution
Step 1

Given :

y=3x+2 

a.

here , 

y is dependent on x 

x is independent variable , and y is dependable variable 

Therefore we write input first (independent variable )  and then its output  (dependable variable  ) 

Hence, ( x , y )

 

 

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