We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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.

Guest Oct 19, 2017

#1**+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.

hectictar Oct 20, 2017

#1**+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