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Question
From the curve y = x, draw y = `1/2 x + 1`
Solution
| x | 0 | 1 | 2 | 3 | − 1 | − 2 | − 3 |
| y | 0 | 1 | 2 | 3 | − 1 | − 2 | − 3 |
y = `1/x + 1`
When x = 0 ⇒ y = `1/2` × 0 + 1 = 1
x = 2 ⇒ y = `1/2` × 2 + 1 = 2
x = 4 ⇒ y = `1/2` × 4 + 1 = 2 + 1 = 3
x = 6 ⇒ y = `1/2` × 6 + 1 = 3 + 1 = 4
x = – 2 ⇒ y = `1/2` × – 2 +1= – 1 + 1 = 0
x = – 4 ⇒ y = `1/2` × – 4 + 1 = – 2 + 1 = – 1
x = – 6 ⇒ y = `1/2` × – 6 + 1 = – 3 + 1 = – 2
| x | 0 | 2 | 4 | 6 | − 2 | − 4 | − 6 |
| y | 1 | 2 | 3 | 4 | 0 | − 1 | − 2 |
The graph of y = `1/2x + 1` stretches the graph y = x towards the x-axis since the multiplying factor is `1/2` which is less than 1 and shifts to the upward by 1 unit.
The graph of y = kf(x), k > 0 moves towards the x-axis if k is less than 1.
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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