Question

The graph of y = 1 x is vertically stretched by a factor of 3, reflected across the y-axis and shifted to the left by 2 units. What is the function of the resulting graph? A) y = 3 x − 2 B) y = −3 x + 2 C) y = 1 3x − 6 D) y = −1

Answer 1

y = 3(-x - 2)

Any horizontal transformations or reflections you make to y = x must be within the parentheses.

Answer 2

The transformed function is g(x) = -7
`log_6` (-x) +2

The given base function is

f(x) =
`log_6` (x)

Then we have to find the transformed function.

First of all, the graph of the base function f(x) =
`log_6` (x) is vertically stretched by a factor of 7, then the newly transformed function becomes y = 7
`log_6`(x)

Then the graph of y = 7
`log_6`(x) is reflected over the x-axis, then the newly transformed function becomes y = -7log6(x)

Then the graph of y = -7
`log_6`(x) is reflected over the y-axis, then the newly transformed function becomes y = -7
`log_6`(-x)

And finally, the graph of y=7log6(-x) is vertically shifted up by 2 units, then the newly transformed function becomes

y = -7
`log_6` (-x) +2

which is the required equation for the transformed function.