course Mth 163
Sketch a graph of y = x^2, from x = -3 to x = 3. Then sketch a graph of y = 4 x^2 over the same domain.Description of graphs: Y=x^2 is much wider than y=4x^2 because adding that factor stretches the graph vertically making it more narrow.
•By what factor do we vertically stretch the first graph to obtain the second? We stretched the first graph by a factor of four but by looking at the table it was realistically a factor of 16.
The factor was only 4 (see note below).
•What are the three basic points of the first graph ?(-1,1)(0,0) (1,1)
•What are the three basic points of the second graph? (-1,16)(0,0)(1,16)
When x = 1 we have y = 4 x^2 = 4 * 1^2 = 4 * 1 = 4, not 16.
You might have made an order-of-operations error here and done y = (4 x)^2; for that function your answers would be correct.
Sketch the second graph shifted -.25 units in the x direction and -1.25 units in the y direction.
Description of graph: The graph looks the same it is just moved negatively -.25 units to the left and down -1.25 units
What are the three basic points of this graph?(-1.25,2.25)(-.25,-1.25)(1.25,2.25)
If f(x) = x^2, then what are
• f(x--.25)= (x--.25)^2= x^2-.0625
(x--.25)^2 = (x + .25)^2 = x^2 + .5 x +.0625.
(x-.25)^2 = (x - .25)^2 = x^2 - .5 x +.0625.
In both cases you get an x term, and in neither case do you get -.0625.
• f(x) + -1.25= x^2-1.25
• 4 f(x)=4(x^2)
• 4 f(x--.25) + -1.25= 4((x--.25)^2)-1.25
See my notes; I think you'll understand, and if so you don't need to submit a revision. However if not:
&#Please see my notes and submit a copy of this document with revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end). &#