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Tpy6a [65]
3 years ago
7

Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x)= −1x + 1

Mathematics
2 answers:
Simora [160]3 years ago
8 0

They have the same slope. The slope of f(x) is 3 because it is the m in f(x)=mx+b. In the graph of g(x), the slope can be found by change in y divided by change in x, or rise over run. Between x=0 and x=1, the y value increases by three, from 2 to 5. The slope of g(x) is 3/1=1.

Hope this helps!

Arlecino [84]3 years ago
6 0

Answer with explanation

The Function , f(x)= -1 x +1

Slope of f(x)=-1

Equation of function , g(x),that is, line passing through ,(0,3) and (2,-1) can be obtained by

Equation of line passing through two points , (x_{1},y_{1}), (x_{2},y_{2}) is,

      \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

→\frac{y-3}{x-0}=\frac{3+1}{0-2}\\\\ \frac{y-3}{x}=\frac{4}{-2}\\\\y-3=-2 x\\\\ 2 x+y=3

g(x)= 2 x+y=3

y= -2 x+3

Slope of g(x)= -2  

-1 > -2

So, Slope of f(x) > Slope of g(x)

Option a: The function f(x) has a larger slope.

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304

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Answer:

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Only the last two options are true.

The first one is false, because 4.5 is the value of the maximum of f(x), not the point where it is reached.

The second one is false, because g(x) has a maximum of 9, so it is a downward-facing parabola (just like f(x)), so it doesn't have a minimum.

The third one is true, because the maximum value of f(x) is 4.5, and the maximum value of g(x) is 9, which is twice the maximum of f(x)

The last one is false (see point 2).

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