Question

c. describe the transformation from the solid function to the dashed function and write
the horizontal asymptote of the dashed function.

transformation:
horizontal asymptote:

transformation:
horizontal asymptote:

transformation:
horizontal asymptote:

Explanation:

Step1: Analyze first graph pair

The solid function is a decreasing exponential with horizontal asymptote $y=0$. The dashed function is shifted down 3 units and reflected over the x-axis.

Step2: Find first asymptote

For the transformed dashed function, the horizontal asymptote shifts to $y=-3$.

Step3: Analyze second graph pair

The solid function has asymptote $y=0$. The dashed function is shifted down 2 units and reflected over the x-axis.

Step4: Find second asymptote

The horizontal asymptote of the dashed function is $y=-2$.

Step5: Analyze third graph pair

The solid function has asymptote $y=0$. The dashed function is shifted up 2 units.

Step6: Find third asymptote

The horizontal asymptote of the dashed function is $y=2$.

Answer:

First Graph:

Transformation: Reflected over x-axis, shifted down 3 units
Horizontal Asymptote: $y=-3$

Second Graph:

Transformation: Reflected over x-axis, shifted down 2 units
Horizontal Asymptote: $y=-2$

Third Graph:

Transformation: Shifted up 2 units
Horizontal Asymptote: $y=2$