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3 years ago

What can you learn about a situation from looking at a graph

1 answer:

4 0

You can learn the rate for something by looking at the slope of a graph. You can also look at the start-up fee or initial cost by looking at the y-intercept of the graph. Additionally, you can get an idea of whether you are making a profit or loss in a business, how far you can throw, or many other real life situations.

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Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

2 years ago

Which clipboard (A, B, or C) represents a 270 degree counter- clockwise rotation?

nignag [31]

Answer: C

Step-by-step explanation:

Because if you look at the star then it will show you how it rotated.

5 0

3 years ago

Read 2 more answers

-5 x + y = - 21 and y = x - 1 solve the system of equation

Kitty [74]

Answer:

Step-by-step explanation:

-5x + (x -1) = -21

-4x = -20

x = 5

3 0

3 years ago

You have 2 orange picks for every 5 green. If there are 21 picks in all how many picks are orange

Ronch [10]

15 picks are oranges

Answer:

2 ORANGE = 5 GREEN

GREEN = 2/5 ORANGE = 0.4 ORANGE

---

ORANGE + GREEN = 21

ORANGE + 0.4 ORANGE = 21

1.4 ORANGE = 21

ORANGE = 15

4 0

3 years ago

Read 2 more answers

Keelah's clothing store buys coats for $50 and then sells them for $80 .what is the percent of mark up on the price of the coat

meriva

I would say 10% but I'm not really sure

3 0

3 years ago