Question

How do you use the graph of `f(x)=(7/2)^x` to describe the transformation of `g(x)=-(7/2)^(-x+6)`?

Answer 1

See below.

Explanation:

`y=(7/2)^xcolor(white)(88)[1]`

Multiplying by a negative value causes a reflection in the line`y=0`

`y=-(7/2)^xcolor(white)(88)[2]`

Multiply `x` by `-1` causes a rotation about the y axis.

`y=-(7/2)^(-x)color(white)(88)[3]`

Adding a positive value `a` to `x` closes the curve, adding a negative value opens the curve, but the asymptote `y =0` remains.

`y=-(7/2)^(-x+3)color(white)(88)[4]`

Graphs of each individual stage: