The total number of cookies baked by grandma = 96
Number of grandchildren = 8
As given, all cookies were evenly divided among 8 children, let us assume that everyone except Cindy got equal share. So on being divided equally, it becomes, cookies per children.
But, as mentioned that Cindy received 'c' cookies less, so let us suppose Cindy received 'x' cookies.
Expression becomes:
Hence, Cindy received 12-c cookies.
Answer:
A) See attached for graph.
B) (-3, 0) (0, 0) (18, 0)
C) (-3, 0) ∪ [3, 18)
Step-by-step explanation:
Piecewise functions have <u>multiple pieces</u> of curves/lines where each piece corresponds to its definition over an <u>interval</u>.
Given piecewise function:
Therefore, the function has two definitions:
When <u>graphing</u> piecewise functions:
<u>First piece of function</u>
Substitute the endpoint of the interval into the corresponding function:
Place an open circle at point (3, 0).
Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.
<u>Second piece of function</u>
Substitute the endpoint of the interval into the corresponding function:
Place an closed circle at point (3, 2).
Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.
See attached for graph.
<h3><u>Part B</u></h3>The x-intercepts are where the curve crosses the x-axis, so when y = 0.
Set the <u>first piece</u> of the function to zero and solve for x:
Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.
Set the <u>second piece</u> to zero and solve for x:
Therefore, the x-intercept for the second piece is (18, 0).
So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).
<h3><u>Part C</u></h3>From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.
Interval notation: (-3, 0) ∪ [3, 18)
Learn more about piecewise functions here:
