Question

The graph of g(x) is the graph of f(x)=x^2 shifted 4 units left, vertically stretched by a factor of 3, then shifted 5 units up. What is the function rule for g(x)?

Answer 1

I would say,
\[1/3 (x + 4)^2 + 5\] if stretched means do it wider horizontally.

Answer 2

wow im really dumb thanks i just spent 15 min trying to figure how x^2 fits into the equation thanks!

Answer 3

;)

Answer 4

Actually, \(\dfrac{1}{3} (x + 4)^2 + 5\) would be a VERTICAL SHRINK (some texts call it a "compression") by a factor of three; neither a vertical nor a horizontal stretch.

To make it "wider horizontally" would be a horizontal stretch - that isn't what is asked for here. (That would require changing the coefficient of x, inside the parens.)

In general:

\(\Large y=a\cdot f(x)\) is a vertical STRETCH of f(x) if |a|>1, and a vertical SHRINK of f(x) if |a|<1.

Answer 5

But the (x+4) and the +5 are correct - those give you the horizontal shift, and the vertical shift!

Answer 6

So stretch means make the function sharper. I mistake the terms then. ;)

Answer 7

\(f(x-c)\) shifts \(f(x)\) horizontally
\(f(x)+k\) shifts \(f(x)\) vertically

Answer 8

So wait it's 3(x+4)^2+5?

Answer 9

Right. :)

Answer 10

Oh okay thanks!

Answer 11

You can see the differences here (original in red, stretch in orange, shrink in yellow).
http://kevinmehall.net/p/equationexplorer/#3x^2 |x^2|%281/3%29x^2|[-10,10,-10,10]

Answer 12

oops, link didn't come through properly, but you can c&p it if interested. :)

Answer 13

Got it so the vertical makes it 3 instead of 1/3 got it!

Answer 14

Yeah, that is the reason I put " if stretched means do it wider horizontally", but it was just the opposite :)

Answer 15

Awesome, totally makes sense now, thanks you guys! Totally gonna nail my semester test!

Answer 16

tomorrow!

Answer 17

It was only question on review i had trouble with :)