Respuesta :
The parent function is:
[tex]y= \frac{1}{x} [/tex]
The transformed function is:
[tex] \frac{1}{2x-10}-3 \\ \\ = \frac{1}{2(x-5)}-3 \\ \\ = \frac{1}{2}( \frac{1}{x-5} ) -3[/tex]
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.
[tex]y= \frac{1}{x} [/tex]
The transformed function is:
[tex] \frac{1}{2x-10}-3 \\ \\ = \frac{1}{2(x-5)}-3 \\ \\ = \frac{1}{2}( \frac{1}{x-5} ) -3[/tex]
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.
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.
