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The table below represents a linear function f(x) and the equation represents a function g(x):
 

x f(x)
-1 -12
0 -6
1 0

 

g(x)

g(x) = 2x + 6

 


Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).

Part B: Which function has a greater y-intercept? Justify your answer.

 Oct 19, 2017

Best Answer 

 #1
avatar+7350 
+2

Let's pick two points off of the table:  (1, 0)  and  (0, -6)

 

slope of  f(x)  =  \(\frac{\text{change in f(x)}}{\text{change in x}}\,=\,\frac{-6 - 0}{0-1}\,=\,\frac{-6}{-1}\,=\,6\)

 

g(x)  =  2x + 6    Notice that this is in slope-intercept form, so we can already tell that its slope is  2 .

 

6 > 2 ,   so the slope of f(x) > the slope of g(x) . f(x) is "steeper" than g(x).

 

----------

 

The y-intercept is the value of the function when  x = 0 .

 

On the table, there is the point  (0, -6) .

So the y-intercept of f(x)  is  -6 .

 

To find the y-intercept of g(x), plug in  0  for  x  and solve for  g(x) .

g(0)  =  2(0) + 6

g(0)  =  6                So the y-intercept of g(x)  is  6 .

 

6 > -6 ,   so the y-intercept of g(x) > the y-intercept of f(x).  g(x) has a greater y-intercept.

 Oct 20, 2017
edited by hectictar  Oct 20, 2017
 #1
avatar+7350 
+2
Best Answer

Let's pick two points off of the table:  (1, 0)  and  (0, -6)

 

slope of  f(x)  =  \(\frac{\text{change in f(x)}}{\text{change in x}}\,=\,\frac{-6 - 0}{0-1}\,=\,\frac{-6}{-1}\,=\,6\)

 

g(x)  =  2x + 6    Notice that this is in slope-intercept form, so we can already tell that its slope is  2 .

 

6 > 2 ,   so the slope of f(x) > the slope of g(x) . f(x) is "steeper" than g(x).

 

----------

 

The y-intercept is the value of the function when  x = 0 .

 

On the table, there is the point  (0, -6) .

So the y-intercept of f(x)  is  -6 .

 

To find the y-intercept of g(x), plug in  0  for  x  and solve for  g(x) .

g(0)  =  2(0) + 6

g(0)  =  6                So the y-intercept of g(x)  is  6 .

 

6 > -6 ,   so the y-intercept of g(x) > the y-intercept of f(x).  g(x) has a greater y-intercept.

hectictar Oct 20, 2017
edited by hectictar  Oct 20, 2017

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