Question

What effect will replacing x with (x+7) have on the graph of the equation y=x^2?

A. slides the graph 7 units down
B. slides the graph 7 units right
C. shrinks the graph by a factor of 7
D. Slides the graph 7 units left

Answer 1

D

Explanation:

Solution:-

- The given question pertains to the translation of a function f ( x ) over the cartesian coordinate system.

- There are certain guidelines that must be followed when performing any translations of any function f ( x ).

Translation Guideline

Vertical shifts

• Up: f ( x ) - > f ( x ) + b
• Down: f ( x ) - > f ( x ) - b

Horizontal shifts

• Left: f ( x ) - > f ( x + a )
• Right: f ( x ) - > f ( x - a )

Where, " a " and " b " are constants for respective horizontal and vertical shifts.

- We can make a generalized form of the translated function f ( x ) to f* ( x ) as follows:

Generalized shift: f ( x ) - > f ( x ± a ) ± b

Where, a: Unit of horizontal shift

b: Unit of vertical shift

- We are given a function f ( x ) defined. We are to replace the variable ( x ) with ( x + 7 ).

`f ( x ) = x^2\\\\f^*(x) = f ( x + 7 ) = (x + 7 )^2`

- Use the above given guidelines to determine the type of shift. Take a look at the Left shift in the horizontal shift section.

- Left shift : f ( x ) -> f ( x + a ) = f ( x + 7 )

Answer: The function f ( x ) is slided a = 7 units to the left!