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Fri 4 May, 2007 09:04 pm
I need help figuring out the following multiple choice question:
Which of the following describes the steps involved in using the graph of y= 3 cos x + 3.
A. Stretch the graph vertically by a factor of 3 and shift it to the left 3 units.
B. Stretch the graph vertically by a factor of 3 and shift it down 3 units.
C. Stretch the graph vertically by a factor of 3 and shift it to the right 3 units.
D. Stretch the graph vertically by a factor of 3 and shift it up 3 units.
y=0
y=3 What do you do?
y=x
y=3x What do you do?
If the graph is
The graph obviously stretches vertically by a factor of three, even if you didn't know that, it is in every possible solution.
Consider:
y1 = constant
and
y2 = constant + 3
What happens to the graph when we add three?
Then:
y3 = x
and
y4 = x + 3
If you cant see how the graph changes, try seeing what values you get out from each one when you plug in a certain value. How do they differ? For example, put x = 5, then
y3 = 5
and
y4 = 8
and so on. Can you see how this relates to
y = 3 + 3*cos(x)?
Unless of course the graph is y = 3*cos(x+3) which is a different story.
In general, given y = A * f(Bx + C) + D
A stretches/compresses vertically (negative reflects across x-axis)
B stretches/compresses horizontally (negative reflects across y-axis)
C shifts horizontally
D shifts vertically
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