A horizontal stretching is the stretching of the graph away from the y-axis. When a function is horizontally stretched by a factor, k, the x-value of the function is multiplied by the factor k.
Thus, given the parent function

, a horizontal stretch by a factor of

means that the x-value of the function is multiplied by

.
Thus, after a horizontal stretch by a factor of

of the parent function

, we have

.
Refrection of the graph of a function over the y-axis results from adding minus to the x-term of the function.
Thus given the function,

, refrection over the y-axis will result to the function

.
Therefore, <span>the equation of the function that will result when the parent function, </span><span>

, is horizontally stretched by a factor of </span><span>

and reflected over the y-axis is </span>

.