course mth 163
Is this how you submit these quizzes? I'm not sure.
Sketch a graph of y = x^2, from x = -3 to x = 3. Then sketch a graph of y = 3 x^2 over the same domain. By what factor do we vertically stretch the first graph to obtain the second?
we stretch it by a factor of 3.
What are the three basic points of the first graph (i.e., the vertex and the points 1 unit to the right and left of the vertex)?
(0,0) (1,1) and (-1,1)
What are the three basic points of the second graph?
(0,0) (-1,3) and (1,3)
good
Sketch the second graph shifted 1.25 units in the x direction and -1.25 units in the y direction.
What are the three basic points of this graph?
(0,0) (.25, 4.25) (2.25, 4.25)
(0,0) isn't on the stretched and shifted graph. That point would shift +1.25 units in the x direction and -1.25 units in the y, so the vertex would shift to (1.25, -1.25).
The points right and left would be (.25, 1.75) and (2.25, 1.75). It looks like you shifted your points +1.25 in the y direction rather than -1.25.
If f(x) = x^2, then what are
f(x- 1.25)
= (x - 1.25)^2
f(x) + -1.25
=x^2 - 1.25
3 f(x)
3x^2
3 f(x- 1.25) + -1.25?
3(x-1.25)^2 - 1.25"
Good work. I believe you understand this, but you had a couple of easily-corrects errors on the last step of the stretching-shifting process. See my notes. Let me know if you have questions.