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Makovka662 [10]
3 years ago
10

Please help find the formulas for these!! ASAP!!!

Mathematics
1 answer:
Ilya [14]3 years ago
6 0

Answer:

a)\ f(x)=\left\{\begin{array}{cccc}-x+2&for&x\in(0,\ 2]&/0

b)\ f(x)=\left\{\begin{array}{cccc}-3x-3&for&x\in(-1,\ 0]&/-1

Step-by-step explanation:

These are graphs of piecewise functions.

Each part is a graph of the linear function.

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept → (0, b)</em>

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

========================================

<h2>a)</h2>

Part 1:

Points (0, 2) → <em>b = 2</em>, and (2, 0).

Calculate the slope:

m=\dfrac{0-2}{2-0}=\dfrac{-2}{2}=-1

Put the value of <em>m</em> and <em>b</em> to the equation of a line:

(1)\ y=-1x+2=-x+2

Part 2:

Points (2, 1) and (5, 0).

Calculate the slope:

m=\dfrac{0-1}{5-2}=\dfrac{-1}{3}=-\dfrac{1}{3}

Put the value of the slope and the coordinates of the point (5, 0) to the equation of a line:

0=-\dfrac{1}{3}(5)+b

0=-\dfrac{5}{3}+b         <em>add 5/3 to both sides</em>

\dfrac{5}{3}=b

Therefore we have:

y=-\dfrac{1}{3}x+\dfrac{5}{3}

The domain of the function is (0, 2] and (2, 5].

Formula of the piecewise function:

f(x)=\left\{\begin{array}{cccc}-x+2&for&x\in(0,\ 2]&/0

============================================================

<h2>b)</h2>

We solve the same as in a) in Part 1

Part 1:

(-1, 0), (0, -3) → <em>b = -3</em>

m=\dfrac{-3-0}{0-(-1)}=\dfrac{-3}{1}=-3

y=-3x-3

Part 2:

(0, 3) → <em>b = 3</em>, (2, -1)

m=\dfrac{-1-3}{2-0}=\dfrac{-4}{2}=-2

y=-2x+3

Domain: (-1, 0] and (0, 2].

f(x)=\left\{\begin{array}{cccc}-3x-3&for&x\in(-1,\ 0]&/-1

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