#$&*
course Mth 163
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?
**The graph is stretched vertically by 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)?
**(-1,1)(0,0)(1,1)
• What are the three basic points of the second graph?
**(-1,3)(0,0)(1,3)
Sketch the second graph shifted 1.75 units in the x direction and -.75 units in the y direction.
What are the three basic points of this graph?
**(0.25, 0.25)(1.75,-0.75)(3.5, 0.25)
If f(x) = x^2, then what are
• f(x- 1.75), f(x) + -.75, 3 f(x) and 3 f(x- 1.75) + -.75?
**For f(x-1.75), the graph is shifted to the right, where y would be zero at x of 1.75
**For f(x)+-0.75, the graph is down, where x is zero at y of -0.75
**For 3 f(x), the graph vertex is positioned at (0,0) but the original points for 1 and -1 are changed from 1 to 3.
**For 3 f(x-1.75)+-0.75, the graph is shifted to the right and down, combining the first two functions.
"
&#Your work looks very good. Let me know if you have any questions. &#