Find the x and y Intercepts y=(1/2)^(x-3)

$y = {(\frac{1}{2})}^{x - 3}$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = {(\frac{1}{2})}^{x - 3}$

Solve the equation.

Rewrite the equation as ${(\frac{1}{2})}^{x - 3} = 0$ .

${(\frac{1}{2})}^{x - 3} = 0$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln ({(\frac{1}{2})}^{x - 3}) = \ln (0)$

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

There is no solution for ${(\frac{1}{2})}^{x - 3} = 0$

No solution

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = {(\frac{1}{2})}^{(0) - 3}$

Solve the equation.

Remove parentheses.

$y = {(\frac{1}{2})}^{0 - 3}$

Remove parentheses.

$y = {(\frac{1}{2})}^{(0) - 3}$

Simplify ${(\frac{1}{2})}^{(0) - 3}$ .

Subtract $3$ from $0$ .

$y = {(\frac{1}{2})}^{- 3}$

Change the sign of the exponent by rewriting the base as its reciprocal.

$y = 2^{3}$

Raise $2$ to the power of $3$ .

$y = 8$

y-intercept(s) in point form.

y-intercept(s): $(0, 8)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 8)$

Step 4