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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

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

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

Undefined

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

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 $y$ .

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

Solve the equation.

Remove parentheses.

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

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

Apply the product rule to $\frac{1}{3}$ .

$y = \frac{1^{0}}{3^{0}}$

Anything raised to $0$ is $1$ .

$y = \frac{1}{3^{0}}$

Anything raised to $0$ is $1$ .

$y = \frac{1}{1}$

Divide $1$ by $1$ .

$y = 1$

y-intercept(s) in point form.

y-intercept(s): $(0, 1)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 1)$

Step 4