Rhonda is using the total cost of the item ($85.00) multiplied by the discount (10%) to find the total discount: 85 x 0.10 = 8.50. Once Rhonda subtracts the discount ($8.50) from the total: $85 - $8.50 = $76.50. The other way to look at the problem, is that Rhonda is only paying for 90% of the total cost of the items, instead of 100% since she is receiving the 10% discount. So, she would get the same final total by multiplying the cost of the items ($85.00) by 90%, or 0.90.
f(x + 5) = |x + 5|, represents the requested change of 5 units to the left,
f(x) - 4 = |x| - 4, represents the requested change of 4 units down.
Step-by-step explanation:
The following rules will permit you to predict the equation of a new function after applying changes, especifically translations, that shift the graph of the parent function in the vertical direction (upward or downward) and in the horizontal direction (left or right).
<u>Horizontal shifts:</u>
Let the parent function be f(x) and k a positive parameter, then f (x + k) represents a horizontal shift of k units to the left, and f (x - k) represents a horizontal shift k units to the right.
<u>Vertical shifts</u>:
Let, again, the parent function be f(x) and, now, h a positive parameter, then f(x) + h represents a vertical shift of h units to upward, and f(x - h) represents a vertical shift of h units downward.
<u>Combining the two previous rules</u>, you get that f (x + k) + h, represents a vertical shift h units upward if h is positive (h units downward if h is negative), and a horizontal shift k units to the left if k is positive (k units to the right if k negative)
Hence, since the parent function is f(x) = |x|
f(x + 5) = |x + 5|, represents the requested change of 5 units to the left,
f(x) - 4 = |x| - 4, represents the requested change of 4 units down.
Furthermore:
f(x + 5) - 4 = |x + 5| - 4, represents a combined shift 5 units to the left and 4 units down.
