Algebra Examples

$f (x) = \frac{24}{1 + 3 e^{- 1.3 x}}$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = \frac{24}{1 + 3 e^{- 1.3 x}}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$24 = 0$

Step 1.2.2

Since $24 \neq 0$ , 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.

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Step 2.1

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

$y = \frac{24}{1 + 3 e^{- 1.3 \cdot 0}}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{24}{1 + 3 e^{- 1.3 \cdot 0}}$

Step 2.2.2

Simplify $\frac{24}{1 + 3 e^{- 1.3 \cdot 0}}$ .

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Step 2.2.2.1

Simplify the denominator.

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Step 2.2.2.1.1

Multiply $- 1.3$ by $0$ .

$y = \frac{24}{1 + 3 e^{0}}$

Step 2.2.2.1.2

Anything raised to $0$ is $1$ .

$y = \frac{24}{1 + 3 \cdot 1}$

Step 2.2.2.1.3

Multiply $3$ by $1$ .

$y = \frac{24}{1 + 3}$

Step 2.2.2.1.4

Add $1$ and $3$ .

$y = \frac{24}{4}$

Step 2.2.2.2

Divide $24$ by $4$ .

$y = 6$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 6)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 6)$

Step 4