Consider the graph given below.

determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above.

shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2

shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2 reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units

shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6

shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2

reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units

Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units.

Step-by-step explanation:

Given:

The parent function is given as:

Now, let us find the equation of the transformed function using the graph.

Slope of the graph is given as the ratio of the y intercept and x intercept.

y-intercept = 6

x-intercept = 3

Therefore, slope is,

Negative sign means that the 'y' value decreases as 'x' increases.

Now, equation of a line with slope 'm' and y intercept 'b' is given as:

Plug in -2 for 'm' and 6 for 'b'. This gives,

So, the parent function is transformed to .

Now, let us transform the parent function to using the rules of transformation.

1. Multiplying the parent function by -1.

This is reflection over the x axis.

2. Multiplying by 2.

This transformation vertically stretches by a factor of 2.

3. Now, add 6 to .

This shifts the graph up by 6 units.

Therefore, the series of transformations are:

Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units.

you can use a^2+ b^2=c^2