Question

When the equation is f(x+h), what is the translation?

Answer 1

When the equation is f(x+h), it represents a translation of the function f(x) horizontally to the left or right. The value of h determines the direction and magnitude of the translation.

If h is positive, the graph of f(x) is shifted horizontally to the left by |h| units. This means that every point on the graph will move to the left, making the function appear "delayed" or "shifted to the left."

If h is negative, the graph of f(x) is shifted horizontally to the right by |h| units. In this case, every point on the graph will move to the right, causing the function to appear "advanced" or "shifted to the right."

In summary, the equation f(x+h) represents a horizontal translation of the function f(x), with the value of h determining the direction and distance of the shift.

Answer 2

a shift of h units left

Explanation:

given f(x) then f(x± h) is a horizontal translation of h units

• if + h then a shift left of h units

• if - h then a shift right of h units

then

f(x + h) is a shift of h units to the left