Ezichael John
Jun 6
Since y=log 2 X is equivalent rlto x=2^y,we Draw the graph of the logarithm function by drawing the graph of its equivalent function x=2^y?
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ChatGPT
Jun 6
To graph the function x=2^y, we can start by creating a table of values:
y | x
0 | 1
1 | 2
2 | 4
3 | 8
-1 | 1/2
-2 | 1/4
Plotting these points on a graph, we can see that the function x=2^y is an exponential function that increases rapidly as y increases. The graph will start at the point (0,1) and approach the x-axis as y approaches negative infinity.
Since y=log2(x) is the inverse function of x=2^y, the graph of y=log2(x) will be a reflection of the graph of x=2^y across the line y=x. This means that the graph of y=log2(x) will start at the point (1,0) and increase slowly as x increases.
In summary, the graph of y=log2(x) will be a slowly increasing curve that starts at the point (1,0) and approaches positive infinity as x approaches positive infinity.
y | x
0 | 1
1 | 2
2 | 4
3 | 8
-1 | 1/2
-2 | 1/4
Plotting these points on a graph, we can see that the function x=2^y is an exponential function that increases rapidly as y increases. The graph will start at the point (0,1) and approach the x-axis as y approaches negative infinity.
Since y=log2(x) is the inverse function of x=2^y, the graph of y=log2(x) will be a reflection of the graph of x=2^y across the line y=x. This means that the graph of y=log2(x) will start at the point (1,0) and increase slowly as x increases.
In summary, the graph of y=log2(x) will be a slowly increasing curve that starts at the point (1,0) and approaches positive infinity as x approaches positive infinity.
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Google Gemini AI
Jun 6
Steps to graph the logarithm function using its equivalent function:
1. Plot the points for the equivalent function x = 2^y:
- For y = -1, x = 2^-1 = 1/2
- For y = 0, x = 2^0 = 1
- For y = 1, x = 2^1 = 2
- For y = 2, x = 2^2 = 4
- For y = 3, x = 2^3 = 8
2. Plot these points on the coordinate plane:
- (1/2, -1)
- (1, 0)
- (2, 1)
- (4, 2)
- (8, 3)
3. Connect the points with a smooth curve:
The resulting curve is the graph of the equivalent function x = 2^y.
4. Sketch the inverse relationship:
Since y = log2 x is the inverse of x = 2^y, its graph is a reflection of the graph of x = 2^y across the line y = x.
- Swap the x and y coordinates of each point:
- (1/2, -1) becomes (-1, 1/2)
- (1, 0) becomes (0, 1)
- (2, 1) becomes (1, 2)
- (4, 2) becomes (2, 4)
- (8, 3) becomes (3, 8)
- Plot the reflected points and connect them with a smooth curve.
The resulting curve is a mirror image of the graph of x = 2^y over the line y = x. This is the graph of the logarithm function y = log2 x.
1. Plot the points for the equivalent function x = 2^y:
- For y = -1, x = 2^-1 = 1/2
- For y = 0, x = 2^0 = 1
- For y = 1, x = 2^1 = 2
- For y = 2, x = 2^2 = 4
- For y = 3, x = 2^3 = 8
2. Plot these points on the coordinate plane:
- (1/2, -1)
- (1, 0)
- (2, 1)
- (4, 2)
- (8, 3)
3. Connect the points with a smooth curve:
The resulting curve is the graph of the equivalent function x = 2^y.
4. Sketch the inverse relationship:
Since y = log2 x is the inverse of x = 2^y, its graph is a reflection of the graph of x = 2^y across the line y = x.
- Swap the x and y coordinates of each point:
- (1/2, -1) becomes (-1, 1/2)
- (1, 0) becomes (0, 1)
- (2, 1) becomes (1, 2)
- (4, 2) becomes (2, 4)
- (8, 3) becomes (3, 8)
- Plot the reflected points and connect them with a smooth curve.
The resulting curve is a mirror image of the graph of x = 2^y over the line y = x. This is the graph of the logarithm function y = log2 x.
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