If the parent function y= csc x goes through a transformation to produce 1+csc (x-π), what is the resultant shift in the functio
n’s graph?
1 answer:
The transformations which have made to produce the function
y₂ = 1+csc (x-π) from the <span>parent function y = csc x
</span>1. shift up one unit ⇒ shift one unit in the direction of positive y
2. shift to the left equal to π ⇒ shift π units in the direction of positive x
See the attached figure.
Blue graph represents the parent function
Red graph represents the produced function after transformation.
y₂ = 1+csc (x-π) from the <span>parent function y = csc x
</span>1. shift up one unit ⇒ shift one unit in the direction of positive y
2. shift to the left equal to π ⇒ shift π units in the direction of positive x
See the attached figure.
Blue graph represents the parent function
Red graph represents the produced function after transformation.
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Answer:
vertex = (- 5, - 8)
Step-by-step explanation:
Given a quadratic in standard form : ax² + bx + c = 0 : a ≠ 0
Then the x- coordinate of the vertex is
= -
Given x² + 10x = - 17 ( add 17 to both sides )
x² + 10x + 17 = 0 ← in standard form
with a = 1, b = 10, c = 17, then
= -
= - 5
Substitute x = - 5 into the quadratic for the corresponding value of y
y = (- 5)² + 10(- 5) + 17 = 25 - 50 + 17 = - 8
Hence vertex = (- 5, - 8)