Answer:
- 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.
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.
Answer:
m= 9/5 n - 3
Step-by-step explanation:
Let's solve for m.
−5m+9n=15
Step 1: Add -9n to both sides.
−5m+9n+−9n=15+−9n
−5m=−9n+15
Step 2: Divide both sides by -5.
-5m/-5 = -9n+15/-5
m= 9/5 n - 3
Answer:
0
Step-by-step explanation:
3x^2 + y ( If x = 1, and y = -3)
= 3(1)^2 + (-3)
= 3 + -3
= 0
Cheers.
