The point is on the graph of y=g(x+1)−3 is (−4,2) .
Explanation of Solution
Given information: (−3,5) is a point on the graph of y=g(x) .
Calculation:
What point is on the graph of y=g(x+1)−3 ?
Here,
g(x)=g(x+1)[the graph is shifted with 1 unit to the left.]⇒(−3,5)→(−3−1,5)=(−4,5)
g(x+1)→g(x+1)−3⇒(−4,5)→(−4,5−3)=(−4,2)
Hence, the point is on the graph of y=g(x+1)−3 is (−4,2) .
(b)
To determine
To find: The point on the graph.
(b)
Expert Solution
Answer to Problem 93AYU
The point on the graph of y=−3g(x−4)+3 is (1,−12) .
Explanation of Solution
Given information: (−3,5) is a point on the graph of y=g(x) .
Calculation:
What point on the graph of y=−3g(x−4)+3 ?
Here,
f(x)→g(x−4)[The graph is shifted with 4 units to the right]⇒(−3,5)→(−3+4,5)=(1,5)⇒g(x−4)→3g(x−4)[the graph is shifted by 3]⇒(1,5)→(1,3.5)=(1,15)⇒3g(x−4)→−3g(x−4)[the graph is reflected over the ox−axis]⇒(1,15)→(1,−15)⇒−3g(x−4)→−3g(x−4)+3[the graph is shifted up with 3 units]⇒(1,−15)→(1,−15+3)=(1,−12)
Hence, the point on the graph of y=−3g(x−4)+3 is (1,−12) .
(c)
To determine
To find: The point on the graph.
(c)
Expert Solution
Answer to Problem 93AYU
The point is on the graph of y=g(3x+9) is (−10,5) .
Explanation of Solution
Given information: (−3,5) is a point on the graph of y=g(x) .
Calculation:
What point is on the graph of y=g(3x+9) ?
Here,
g(x)=g(3x)[the graph shinks by 3]⇒(−3,5)→(−1,5)⇒g(3x)→g(3x+9)[the graph is shifted with 9 units to the left]⇒(−1,5)→(−1−9,5)=(−10,5)
Hence, the point is on the graph of y=g(3x+9) is (−10,5) .
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