Question

starting with the graph of f(x)=8^x write the equation of the graph that results from Shifting f(x) 5 units upward y=____shifting f(x) 9 units to the left y=____reflecting f(x) about the x axis and the y axis y=

Answer 1

We have the following:

$f(x)=8^x$

(a)

for there to be an upward displacement, we must add the function the value that we want it to rise, like this

$f(x)=8^x+5$

(b)

for there to be a shift to the left, we must add the exponent from the value we want it to rise, like this

$f(x)=8^{x+9}$

(c)

for there to be a shift to the left, we must subtract the exponent from the value we want it to rise, like this

The inverse is:

$\begin{gathered} y=8^x \\ x=8^y \\ \ln x=y\cdot\ln 8 \\ y=\frac{\ln x}{\ln 8} \end{gathered}$

The answer is

$f(x)=\frac{\ln x}{\ln 8}$