Question

Given the function f(x) = 3x + 6 and g(x), which function has a greater slope?

x g(x)
1 3
2 6
3 9
A. f(x) has a greater slope.
B. g(x) has a greater slope.
C. The slopes of f(x) and g(x) are the same.
D. The slope of g(x) is undefined.

Answer 1

Both f(x) and g(x) have the same slope, which is 3. This is calculated using the slope formula for g(x) and by observing the coefficient of x in f(x).

Step-by-step explanation:

The question asks which function, f(x) = 3x + 6 or g(x), has a greater slope. To determine the slope of g(x), we can use two points given from the function's values: (1,3) and (2,6). The slope (m) is determined using the formula m = (y2 - y1) / (x2 - x1). For g(x), the slope is (6 - 3) / (2 - 1) = 3 / 1 = 3. Since the slope of f(x) is also 3 (as it is the coefficient of x in the equation), the slopes are the same. Therefore, the correct option is C. The slopes of f(x) and g(x) are the same.

Answer 2

C. The slopes of f(x) and g(x) are the same.

Explanation:

`\displaystyle 9 = 3[3]`☑

`\displaystyle 6 = 3[2]`☑

`\displaystyle 3 = 3[1]`☑

Therefore we KNOW that the g(x) function ALSO has a rate of change [slope] of 3. With that being said, both functions are parallel, which means they have SIMILAR SLOPES.

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