Identify the type of transformations present for each of the logarithmic functions listed below given the following parent function: y=log3x𝑦=log3𝑥y=−log3(2x)𝑦=−log3(2𝑥)Answer 1 Question 9y=log3(x+1)−4𝑦=log3(𝑥+1)−4Answer 2 Question 9y=2log3x𝑦=2log3𝑥Answer 3 Question 9y=12log3(x)𝑦=12log3(𝑥)Answer 4 Question 9
Question
Identify the type of transformations present for each of the logarithmic functions listed below given the following parent function: y=log3x𝑦=log3𝑥y=−log3(2x)𝑦=−log3(2𝑥)Answer 1 Question 9y=log3(x+1)−4𝑦=log3(𝑥+1)−4Answer 2 Question 9y=2log3x𝑦=2log3𝑥Answer 3 Question 9y=12log3(x)𝑦=12log3(𝑥)Answer 4 Question 9
Solution
Answer 1: The function y=-log3(2x) is a reflection of the parent function y=log3x over the x-axis because of the negative sign. The function is also horizontally compressed by a factor of 2.
Answer 2: The function y=log3(x+1)-4 is a horizontal shift of the parent function y=log3x to the left by 1 unit and a vertical shift down by 4 units.
Answer 3: The function y=2log3x is a vertical stretch of the parent function y=log3x by a factor of 2.
Answer 4: The function y=1/2log3(x) is a vertical compression of the parent function y=log3x by a factor of 1/2.
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