Find the x and y Intercepts f(x)=e^(-x)

$f (x) = e^{- x}$

Find the x-intercepts.

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

$0 = e^{- x}$

Solve the equation.

Rewrite the equation as $e^{- x} = 0$ .

$e^{- x} = 0$

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

$\ln (e^{- x}) = \ln (0)$

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

Undefined

There is no solution for $e^{- x} = 0$

No solution

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

x-intercept(s): $None$

Find the y-intercepts.

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

$y = e^{- (0)}$

Simplify $e^{- (0)}$ .

Multiply $- 1$ by $0$ .

$y = e^{0}$

Anything raised to $0$ is $1$ .

$y = 1$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $None$

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