Find the x and y Intercepts f(x)=20/(1+9e^(3x))

$f (x) = \frac{20}{1 + 9 e^{3 x}}$

Step 1

Find the x-intercepts.

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

$0 = \frac{20}{1 + 9 e^{3 x}}$

Solve the equation.

Set the numerator equal to zero.

$20 = 0$

Since $20 \neq 0$ , there are no solutions.

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 $y$ .

$y = \frac{20}{1 + 9 e^{3 (0)}}$

Solve the equation.

Remove parentheses.

$y = \frac{20}{1 + 9 e^{3 (0)}}$

Simplify $\frac{20}{1 + 9 e^{3 (0)}}$ .

Simplify the denominator.

Multiply $3$ by $0$ .

$y = \frac{20}{1 + 9 e^{0}}$

Anything raised to $0$ is $1$ .

$y = \frac{20}{1 + 9 \cdot 1}$

Multiply $9$ by $1$ .

$y = \frac{20}{1 + 9}$

Add $1$ and $9$ .

$y = \frac{20}{10}$

Divide $20$ by $10$ .

$y = 2$

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 2)$

Step 4