Precalculus Examples

$f (x) = \frac{6}{1 + 2 e^{- x}}$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

$0 = \frac{6}{1 + 2 e^{- x}}$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Set the numerator equal to zero.

$6 = 0$

Step 1.2.2

Since $6 \neq 0$ , there are no solutions.

No solution

Step 1.3

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.

Tap for more steps...

Step 2.1

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

$y = \frac{6}{1 + 2 e^{- (0)}}$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Remove parentheses.

$y = \frac{6}{1 + 2 e^{- (0)}}$

Step 2.2.2

Simplify $\frac{6}{1 + 2 e^{- (0)}}$ .

Tap for more steps...

Step 2.2.2.1

Simplify the denominator.

Tap for more steps...

Step 2.2.2.1.1

Multiply $- 1$ by $0$ .

$y = \frac{6}{1 + 2 e^{0}}$

Step 2.2.2.1.2

Anything raised to $0$ is $1$ .

$y = \frac{6}{1 + 2 \cdot 1}$

Step 2.2.2.1.3

Multiply $2$ by $1$ .

$y = \frac{6}{1 + 2}$

Step 2.2.2.1.4

Add $1$ and $2$ .

$y = \frac{6}{3}$

Step 2.2.2.2

Divide $6$ by $3$ .

$y = 2$

Step 2.3

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