Question

Describe the transformations on the given logarithmic function. [C6] x(x)=−⌊login​∣−⟨(x−7)⌋−85 9. Write the equation of a logarithmic function that has been vertically stretched by 5 , reflected in the x-axis, horizontally compressed by 1/3, moved 11 units left and 8 units down.

Answer 1

The transformed logarithmic function after the given series of transformations would be f(x) = -5log_b(3(x+11)) - 8, representing a vertical stretch by 5, reflection across the x-axis, horizontal compression by 1/3, moving 11 units left, and moving 8 units down.

Step-by-step explanation:

The question involves applying a series of transformations to a logarithmic function. When a function is vertically stretched by a factor of 5, reflected in the x-axis, horizontally compressed by 1/3, translated 11 units to the left, and 8 units down, the transformed function can be written as:

f(x) = -5logb(3(x+11)) - 8

This function starts with the base function logb(x), then:

• Multiplies the output by 5 for the vertical stretch,
• Negates it for reflection in the x-axis,
• Makes the input 3 times faster (compression) by multiplying the x-value inside the function by 3,
• Moves the graph 11 units to the left by adding 11 within the logarithm, and
• Moves it down 8 units by subtracting 8 from the entire function.

Note that 'b' represents the base of the logarithm, which could be any positive number other than 1. The specific value of 'b' is not given, so it remains as a placeholder in the function.