Math Analysis
posted by Emily on .
Given f(x) as shown, graph the following: [the line is going through (2,3) and (2,0)]
1. f(x) + 2
==> My graph I have is a line going through the points (2,1) and (2,2). Is this correct?
2. 2f(x)
==> Can someone help me with this one please? I thought the 2 in front of the f(x) would affect the amplitude of the graph, but I don't see how this graph would have an amplitude.
Any help is GREATLY appreciated!!!!!

OK. The original function is
f(x)=(3/4)x3/2
1. Yes, the function (3/4)x + 1/2 does pass through those points (2,1) and (2,2), as you can verify by plugging them in
2. You're right; there is no amplitude  but there is a slope! It doubles the slope, and the yintercept.
2f(x) = 2(3/4)x2(3/2)
=(3/2)x 3
That passes through (0,3) and (2,0) 
Ohhhh I get it :) I have like two more questions though 
3. f(2x)
==> Would you multiply the x and y coordinates by 2? I'm soooo confused :/
And for number 8, the graph is a parabola instead, with the vertex at (0,0), and the "arms" of the parabola going through the points (1,1), (1,1), and (2,4). A parabola doesn't have an amplitude either, so what exactly would you do here? (don't worry  this isn't all my homework, these are just a few examples so I know how to do the others) 
You don't multiply the coords, exactly. What you're scaling is the coefficients.
But careful: f(2x) is not 2f(x)!
f(2x) means might be a shorthand for f(g(x)), where g(x) = 2x.
2f(x) would be
2(3/4)x+2(3/2)
=3(3/2)x
Your parabola is y=x^2, or
f(x) = x^2
so
2f(x) = 2x^2
and everything else, including the scaling, follows from that.
(1,1) > (1,2)
(1,1) > (1, 2)
(2, 4) > (2, 8)
See? The y value is doubled, which is kind of obvious when you see that you're going from:
y = x^2
to
y = 2x^2
(And don't worry about being confused; that just means you're paying attention. :) 
Ohhhh that makes PERFECT sense! :D I'm soo glad I get this now. Thanks so much!! :)