Graphing f(x) = logSUB2(x), rotating, and writing the eqn of

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This question is three-fold. Ready?

PART A: Graph f(x) = logSUB2(x).

I converted the function above to 2^y = x and selected different values for y to find x. Is this correct?

PART B: On the same xy-plane, ROTATE the graph from PART A 90 degrees counterclockwise about the origin.

PART B threw me totally off. How do I rotate the graph of f(X) = logSUB2(x) about the origin, x-axis or y-axis should I ever see such questions?

PART C: Write an equation of the function graphed in PART B.

This means to CREATE an equation of the ROTATED graph in PART B, right?

How do I come up with an equation based on a graph that has been rotated 90 degrees or any other degree measure?
 
interval said:
PART A: Graph f(x) = logSUB2(x).

I converted the function above to 2^y = x and selected different values for y to find x. Is this correct?
Click to expand...
That's one way and, since you've converted to the correct exponential equivalent, you'll get the same graph. Another way would be to use powers of 2 directly in the log, which is, in essence, doing your way, but backwards:

. . . . .2<sup>0</sup> = 1 => log<sub>2</sub>(1) = 0 => (x, y) = (1, 0)
. . . . .2<sup>1</sup> = 2 => log<sub>2</sub>(2) = 1 => (x, y) = (2, 1)
. . . . .2<sup>2</sup> = 4 => log<sub>2</sub>(4) = 2 => (x, y) = (4, 2)
. . . . .2<sup>3</sup> = 8 => log<sub>2</sub>(8) = 3 => (x, y) = (8, 3)
. . . . .2<sup>-1</sup> = 0.5 => log<sub>2</sub>(0.5) = -1 => (x, y) = (0.5, -1)

...and so forth. These points should look fairly familiar. :wink:

interval said:
PART B: On the same xy-plane, ROTATE the graph from PART A 90 degrees counterclockwise about the origin.
Click to expand...
The origin is where the axes cross; that is, the point (0, 0).

To rotate 90°, think about drawing another x,y-plane. Taking your graph of f(x) = log<sub>2</sub>(x) -- and having drawn this graph very darkly -- put the sheet with this graph underneath your new graph, but rotated one quarter turn anti-clockwise.

You should be able to see the old graph through the top sheet of paper. Line up the origins so they overlap, and make sure the axes line up (though they're pointing in different directions), and trace the old (but rotated) graph onto your new (top) sheet. This is the new graph they want. From your graphing of exponentials, this new graph should look very familiar.

interval said:
How do I rotate the graph...about the origin, x-axis or y-axis should I ever see such questions?
Click to expand...
"About the origin" (or any other point) is covered above. "About" (or "across") an axis just means to flip it over, as though you'd put a skewer through the sheet, along that line, and then twirled the skewer to flip the sheet over. You can see animations of this here.

interval said:
PART C: Write an equation of the function graphed in PART B.
Click to expand...
Hint: What function did you use to create your graph? What would you get if you switched the x's and y's?

Eliz.
 
ok

Stapel,

You provided good math data here.

Your question:

"Hint: What function did you use to create your graph? What would you get if you switched the x's and y's?"

My reply:

The equation is 2^x = y, right? I switched x and y as you suggested.

Is this right?
 
interval said:
The equation is 2^x = y, right? I switched x and y as you suggested. Is this right?
Click to expand...
Graph y = 2<sup>x</sup>, and compare with y = log<sub>2</sub>(x). You should be pleased with the results! :D

Eliz.
 
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