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kirill115 [55]
2 years ago
7

Write a piecewise-defined function that represents the graph?

Mathematics
1 answer:
kodGreya [7K]2 years ago
4 0

Answer:

f(x) = { x, -5 ≤ x < 0 and 3x - 3, 1 ≤ x < 5

Step-by-step explanation:

The equation of one line is y = x

The equation of the other line is y = 3x - 3

Altogether,

f(x) = { x, -5 ≤ x < 0 and 3x - 3, 1 ≤ x < 5

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densk [106]
I need more information about the dimensions of the barn
4 0
3 years ago
f(x)=x^2; vertical shrink by a factor of 1/2 and a reflection in the y-axis, followed by a translation 1 unit down​
NeX [460]

The image of the function f(x) after vertical shrink by a factor of 1/2

and a reflection in the y-axis, followed by a translation 1 unit down​

is g(x) = \frac{1}{2} x² - 1

Step-by-step explanation:

Lets revise:

1. The vertical shrink

A vertical shrinking is the squeezing of the graph toward the x-axis.

if 0 < k < 1 (a fraction), the graph of y = k•f(x) is the graph of f(x) vertically

shrunk by multiplying each of its y-coordinates by k

2. The reflection

If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

3. Vertical translation

If the function f(x) translated vertically up  by m units, then its image

is g(x) = f(x) + m

If the function f(x) translated vertically down  by m units, then its image

is g(x) = f(x) - m

Now let us solve the problem

∵ f(x) = x²

∵ f(x) shrunk by a factor of \frac{1}{2}

∴ The image of f(x) = \frac{1}{2} x²

∵ The image of f(x) reflected across y-axis

∴ The sign of x will change

∴ The new image of f(x) = \frac{1}{2} (-x)²

∵ The new image of f(x) translated 1 unit down

∴ We will subtract the new image of f(x) by 1

∴ The last image of f(x) is g(x) = \frac{1}{2} (-x)² - 1

<em>V.I.Note:</em>

(-x)² = x² because even exponents reject the negative sign

The image of the function f(x) after vertical shrink by a factor of 1/2

and a reflection in the y-axis, followed by a translation 1 unit down​

is g(x) = \frac{1}{2} x² - 1

The attached graph for more understand

Learn more:

you can learn more about transformation in brainly.com/question/2415963

#LearnwithBrainly

4 0
3 years ago
Help&amp;EXPLAIN <br> •••••••••••••••••••<br> Help plz
Stolb23 [73]

Answer:

diameter = 2.5 feet

Step-by-step explanation:

Circumference of a circle is given as C = πd

Circumference of the tree trunk = 7.85 ft

π = 3.14

Diameter of the tree trunk = d

Thus:

7.85 = 3.14*d

Divide both sides by 3.14

7.85/3.14 = 3.14*d/3.14

2.5 = d

d = 2.5 ft

3 0
2 years ago
Find the volume of each cylinder. Use 3.14 for pi. Round your answer to the nearest tenth
otez555 [7]

Answer:

V ≈471.24 mm^3

Step-by-step explanation:

The formula for cylinder volume is πr^2 x h, so ((π x 25) x h). That's just 25π x 6. That is about 471.238898, which rounded is almost 471.24. Or, in terms of π, you could leave your answer as 150π mm^3

8 0
3 years ago
Write the equation g(x) in vertex form of a
DerKrebs [107]

The equation g(x) in vertex form of a  quadratic function for the transformations  whose graph is a  translation 4 units left and 1 unit up of the  graph of f(x) is (x-4)² + 1

Given a  quadratic function for the transformations given  the function f(x) = x²

If the function g(x) of the graph is translated 4 units to the left, the equation becomes (x-4)² (note that we subtracted 4 from the x value

  • Translating the graph 1 unit up will give the final function g(x) as (x-4)² + 1 (We added 1 since it is an upward translation.)

Hence the equation g(x) in vertex form of a  quadratic function for the transformations  whose graph is a  translation 4 units left and 1 unit up of the  graph of f(x) is (x-4)² + 1

Learn more here: brainly.com/question/15381183

8 0
2 years ago
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