Which transformation from the graph of a function f(x) describes the graph of f(x)-1?

Mathematics

1 answer:

andrezito [222]3 years ago

4 0

Answer:

Step-by-step explanation:

Any side to side movement of a function will be reflected inside a set of parenthesis with the x. For example, if the function was a parabola, the parent graph could be, very simply,

$y=x^2$

Side to side movement would make the equation look like this:

$y=(x-h)^2$

where h is the x coordinate of the vertex.

Up or down movment would make the equation look like this:

$y=x^2+k$ for movement upwards, or

$y=x^2-k$ for movement downwards. The k represents the y coordiante of the vertex in this parabola.

Because our function has NO numbers inside the parenthesis with the f(x), but it has a -1 after, we are moving the parent graph of this function, whatever it is, down one from its starting position.

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Please explain how to do #6 i know the work is right but i don’t understand it

mariarad [96]

Since this is part of a packet, there's a lot of prior knowledge you need to understand the question.
1) The angle of elevation is the angle between the horizontal and the light of sight from the object to the observer (see picture 1).

2) A lot of the units are from work done by an Indian astronomer. The line of sight (light blue in picture 1) is r = 3438 (I think you might have forgotten to finish writing the number). r, or 3438, is the distance from the earth to the sun used by Indian Astronomers.

3) The table shows units in jya(θ°). Jya is a Sanskrit (ancient Indian language) word. It stands for the length of half of a chord that connects two endpoints of a circle (kinda confusing and more information than you need to know - but it's the green line in picture 2).
What's important is: jya(θ°) = r*sin(θ°)

Now let's tackle the problem:
1) You know that the angle of elevation is 67.5°. Using the chart, the only important value is the second from the bottom. jya(67.5°) = 3177.

2) Remember that jya(θ°) = r*sin(θ°).
Also remember that sine of an angle is $\frac{opposite}{hypotenuse}$ . In this problem, r, the distance from the earth to the sun, happens to be the hypotenuse of the triangle since its the longest edge.

3) Notice that you're dividing jya(θ°) (aka r*sin(θ°)) by r = 3438. That will give you sin(θ°) by itself. Then you're multiplying that sin(θ°) by 1 AU, which we are told is the actual distance of the hypotenuse/distance from earth to sun. Since sine = $\frac{opposite}{hypotenuse}$ that gives you the apparent length of the opposite side = apparent height of the sun.

The math is a bit weird, but you're basically multiplying sine by the apparent distance 1AU to get the apparent height, instead of multiplying sine by the estimated height r = 3438. Dividing 3177 by 3438 gives you sin(67.5°). Then multiplying sin(67.5°) by the apparent hypotenuse, 1AU, gives you the apparent height. That's how I'm understanding it!