Question

Describe the graph of y=1/2x-10 -3 compared to the graph of y=1/x

Answer 1

The following transformations may be seen when comparing the above simplified code to the parent function:

1) 1/2 multiplication.

Dilation is indicated by multiplying the function by a number. Because the number lies between 0 and 1, the function is compressed by a factor of 2 in the vertical direction.

2) Subtract five from x.

A horizontal movement to the right is indicated by subtracting a number from x. This indicates that the parent function has been shifted 5 units to the right.

3) Remove three from the function.

A downward shift is indicated by subtracting a number from the function. This means the parent function has been reduced by three units.

To obtain the new function, the preceding three transformations are applied to y = 1/x.

Answer 2

The parent function is:


`y= (1)/(x)`

The transformed function is:


`(1)/(2x-10)-3 \\ \\ = (1)/(2(x-5))-3 \\ \\ = (1)/(2)( (1)/(x-5) ) -3`

If we compare the above simplified function with the parent function we can note the following transformations:

1) Multiplication by 1/2
Multiplying the function by a number indicates dilation. Since the number is between 0 and 1, the function is being compressed in vertical direction by a factor of 2.

2) Subtraction of 5 from x.
Subtracting a number from x indicates a horizontal shift towards right. This means the parent function is transformed 5 units to right.

3) Subtraction of 3 from the function.
Subtracting a number from the function indicates a downward shift. This means the parent function is transformed 3 units down.

The above 3 transformations are done on y = 1/x to get the new function.