Draw a line having a slope of 1/3 and y-intercept of -1

Mathematics

1 answer:

Lilit [14]2 years ago

8 0

Equation for slope=1/3 and y-intercept=-1 is:
y = mx + b
where m is slope and b is y-intercept.
So, equation becomes
y = -1x + 1/3
Now put different values of x in the equation to get corresponding value of y.
x     y
0    1/3
1 -2/3
2 -5/3
3 -8/3
-1    4/3
-2    7/3
-3    10/3

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The function of f(x) = 3x + 2 has a domain of -3 < x < 5. What is the domain of f-1(x)?

Flura [38]

<h3>Answer: -7 < x < 17</h3>

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Explanation:

Plug in the lower bound of the domain, which is x = -3

f(x) = 3x+2

f(-3) = 3(-3)+2

f(-3) = -9+2

f(-3) = -7

If x = -3, then the output is y = -7. Since f(x) is an increasing function (due to the positive slope), we know that y = -7 is the lower bound of the range.

If you plugged in x = 5, you should find that f(5) = 17 making this the upper bound of the range.

The range of f(x) is -7 < y < 17

Recall that the domain and range swap places when going from the original function f(x) to the inverse $f^{-1}(x)$

This swap happens because how x and y change places when determining the inverse itself. In other words, you go from y = 3x+2 to x = 3y+2. Solving for y gets us y = (x-2)/3 which is the inverse.

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In short, we found the range of f(x) is -7 < y < 17.

That means the domain of the inverse is -7 < x < 17 since the domain and range swap roles when going from original to inverse.

6 0

3 years ago

A rectangle on a coordinate plane has vertices at (7,5),(-7,5),(-7,-2),and (7,-2) what is the perimeter of the rectangle?

Nadya [2.5K]

Answer:

Your Perimiter is 42

Step-by-step explanation:

Distance from 7,5 to -7,5 is 14

Distance from -7,5 to -7,-2 is 7