Find the x and y Intercepts f(x)=-1/4e^(x-3)

$f (x) = - \frac{1}{4} e^{x - 3}$

Step 1

Find the x-intercepts.

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

$0 = - \frac{1}{4} \cdot e^{x - 3}$

Solve the equation.

Rewrite the equation as $- \frac{1}{4} \cdot e^{x - 3} = 0$ .

$- \frac{1}{4} \cdot e^{x - 3} = 0$

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{1}{4} \cdot e^{x - 3}) = - 4 \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{1}{4} \cdot e^{x - 3})$ .

Combine $e^{x - 3}$ and $\frac{1}{4}$ .

$- 4 (- \frac{e^{x - 3}}{4}) = - 4 \cdot 0$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{e^{x - 3}}{4}$ into the numerator.

$- 4 \frac{- e^{x - 3}}{4} = - 4 \cdot 0$

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- e^{x - 3}}{4} = - 4 \cdot 0$

Cancel the common factor.

$4 \cdot - 1 \frac{- e^{x - 3}}{4} = - 4 \cdot 0$

Rewrite the expression.

$- - e^{x - 3} = - 4 \cdot 0$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 e^{x - 3} = - 4 \cdot 0$

Multiply $e^{x - 3}$ by $1$ .

$e^{x - 3} = - 4 \cdot 0$

Simplify the right side.

Multiply $- 4$ by $0$ .

$e^{x - 3} = 0$

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

$\ln (e^{x - 3}) = \ln (0)$

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

Undefined

There is no solution for $e^{x - 3} = 0$

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 $y$ .

$y = - \frac{1}{4} \cdot e^{(0) - 3}$

Simplify $- \frac{1}{4} \cdot e^{(0) - 3}$ .

Subtract $3$ from $0$ .

$y = - \frac{1}{4} \cdot e^{- 3}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = - \frac{1}{4} \cdot \frac{1}{e^{3}}$

Multiply $\frac{1}{e^{3}}$ by $\frac{1}{4}$ .

$y = - \frac{1}{e^{3} \cdot 4}$

Move $4$ to the left of $e^{3}$ .

$y = - \frac{1}{4 e^{3}}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{4 e^{3}})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{1}{4 e^{3}})$

Step 4

Find the x and y Intercepts f(x)=-1/4e^(x-3)

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