Answer:
The graph of g is the graph of f shifted down 1 unit.
Step-by-step explanation:
Suppose you have a function y = f(x), you can do these following operations on the function:
Shift up a units: y = f(x) + a
Shift down a units: y = f(x) - a
Shift left a units: y = f(x + a)
Shift right a units: y = f(x - a)
In this problem, we have that:
g(x) = -1 + f(x) = f(x) - 1
So the graph of g is the graph of f shifted down 1 unit.
9514 1404 393
Answer:
Step-by-step explanation:
The ratios all have ...
first number : second number = 1 : 4
Using first numbers of 1, 2, 3, the second numbers can be found by multiplying these by 4. (1, 4), (2, 8), (3, 12)
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You plot these (x, y) points the same way you plot <em>any</em> point on a coordinate grid. The first (x) value is the horizontal distance from the vertical axis. Positive is to the right. The second (y) value is the vertical distance from the horizontal axis. Positive is up.
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Of course, the origin is where the horizontal and vertical axes meet. It can be convenient to find one of the coordinates on its respective axis, then use the other coordinate to find the point at the desired distance from that axis.
Usually, you would choose the axis on the basis of how easy it is to determine exactly where the coordinate lies. If the y-axis is marked every 5, for example, it might be hard to determine where a multiple of 4 will lie. Locating the x-coordinate on the x-axis may be an easier way to start.
Say you're trying to figure out what percentage 3 is of 15.
3/15 = x/100
You would cross multiply so..
3(100) = 15x
Then simplify.
300 = 15x
300/15 = 15x/15
20 = x
Therefore, 3 is 20% of 15.
Answer:
The number of ways are 40320.
Step-by-step explanation:
Consider the provided information.
Ms. Smith keeps eight different cookbooks on a shelf in one of her kitchen cabinets.
We need to determine the number of different ways to put eight cookbooks on the shelf.
We need to select 8 cookbooks taking 8 at a time.
So use the permutation formula:
Substitute n=8 and simplify.

Hence, the number of ways are 40320.
It's an example of rotation symmetry, if the image appears unchanged. If the rotation symmetry exists there is a one centre point around which an image appears unchanged.