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.
+9481 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).
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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.
+9481 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.
