The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −9 0 −1 1 7 g(x) g(x) = 3x − 2 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). (6 points) part b: which function has a greater y-intercept? justify your answer. (4 points) (10 points)

Part A: The slope of function is greater than the slope of .

Part B: The function has a greater y-intercept.

Given:

The table of values for the function is:

:      

:        

The equation of second function is .

To find:

Part A: Find the slope of and and then compare them.

Part B: Find the y-intercepts of both functions and then compare them.

Explanation:

Part A:

From the given table it is clear that the function passes through the points and . So, the slope of the function is:

Slope of the function is .

The slope-intercept form of a line is:

Where, is slope and is y-intercept.

Comparing with slope-intercept form, we get

Slope of the function is .

Since , therefore the slope of function is greater than the slope of .

Part B:

The function passes through the point . So, y-intercept of is .

Comparing with slope-intercept form, we get

So, y-intercept of is .

Since , therefore the function has a greater y-intercept.

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Part A: The slope of f(x) is greater than the slope of g(x)

Part B: F(x) has a greater y-intercept.

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Step-by-step explanation:

The table for f(x) is as shown in the attached figure with red color.

g(x) = 3x-2

Part A: Write a sentence to compare the slope of the two functions?

The slope of the line =(y2 - y1)/(x2 - x1)

So, using any two points to find the slope of f(x)

The slope of f(x) is =

For the function g(x) = 3x-2

The slope of g(x) = 3

So, the slope of f(x) is greater than the slope of g(x)

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Part B: Which function has a greater y-intercept?

To find y-intercept put x = 0

For the function f(x)

When x = o ⇒ f(x) = -1  (From the table)

And for the function g(x)

when x = 0 ⇒ g(x) = 3*0 - 2 = -2

So, F(x) has a greater y-intercept.

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0

step-by-step explanation:

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