Question

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)

Answer 1

Answer:

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 = $\frac{-1-(-9)}{0-(-1)} =\frac{8}{1} =8$

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 2

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

Part B: The function $f(x)$ has a greater y-intercept.

Given:

The table of values for the function $f(x)$ is:

$x$ :   $-1$   $0$   $1$

$f(x)$ :    $-9$   $-1$   $7$

The equation of second function is $g(x)=3x-2$.

To find:

Part A: Find the slope of $f(x)$ and $g(x)$ 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 $(-1,-9)$ and $(0,-1)$. So, the slope of the function $f(x)$ is:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{-1-(-9)}{0-(-1)}$

$m=\dfrac{-1+9}{0+1}$

$m=8$

Slope of the function $f(x)$ is $8$.

The slope-intercept form of a line is:

$y=mx+b$

Where, $m$ is slope and $b$ is y-intercept.

Comparing $g(x)=3x-2$ with slope-intercept form, we get

$m=3$

Slope of the function $g(x)$ is $3$.

Since $8>3$, therefore the slope of function $f(x)$ is greater than the slope of $g(x)$.

Part B:

The function $f(x)$ passes through the point $(0,-1)$. So, y-intercept of $f(x)$ is $-1$.

Comparing $g(x)=3x-2$ with slope-intercept form, we get

$b=-2$

So, y-intercept of $g(x)$ is $-2$.

Since $-1>-2$, therefore the function $f(x)$ has a greater y-intercept.

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