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प्रश्न
Write the steps to obtain the graph of the function y = 3(x − 1)2 + 5 from the graph y = x2
उत्तर
Step 1:
Draw the graph y = x2
| x | 0 | 1 | − 1 | 2 | − 2 |
| y | 0 | 1 | 1 | 4 | 4 |
Step 2:
The graph of y = (x – 1)2 shifts to the right for one unit.
| x | 0 | 1 | − 1 | 2 | − 2 | 3 |
| y | 1 | 0 | 4 | 1 | 9 | 4 |
The graph of y = (x – 1)2 shifts the graph
y = x2 to the right by 1 unit.
The graph of y = f(x – c), c > 0 causes the graph y = f(x) a shift to the right by c units.
Step 3:
The graph of y = 3(x – 1)2 compresses towards y-axis that is moves away from the x-axis since the multiplying factor is which is greater than 1.
| x | 0 | 1 | – 1 | 2 | – 2 | 3 |
| y | 3 | 0 | 12 | 3 | 24 | 12 |
The graph of y = 3(x – 1)2 compresses the graph y = (x – 1)2 towards the y-axis that is moving away from the x-axis since the multiplying factor is greater than 1.
For the graph y = kf(x), If k is a positive constant greater than one, the graph moves away from the x-axis.
If k is a positive constant less than one, the graph moves towards the x-axis.
Step 4:
The graph of y = 3(x – 1)2 + 5 causes the shift to the upward for 5 units.
| x | 0 | 1 | – 1 | 2 | – 2 | 3 |
| y | 8 | 5 | 17 | 8 | 32 | 17 |
The graph of y = 3(x – 1)2 + 5 causes the graph y = 3(x – 1)2 shifts to the upward for 5 units.
The graph of y = f(x) + d, d > 0 causes the graph y = f(x) a shift to the upward by d units.
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संबंधित प्रश्न
For the curve y = x3 given in Figure 1.67, draw
y = −x3 
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