Finite Math Examples

$f (x) = {(1 + e^{x})}^{- 4}$

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 $x$ .

$0 = {(1 + e^{x})}^{- 4}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as ${(1 + e^{x})}^{- 4} = 0$ .

${(1 + e^{x})}^{- 4} = 0$

Step 1.2.2

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

$\frac{1}{{(1 + e^{x})}^{4}} = 0$

Step 1.2.3

Set the numerator equal to zero.

$1 = 0$

Step 1.2.4

Since $1 \neq 0$ , 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 $y$ .

$y = {(1 + e^{0})}^{- 4}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = {(1 + e^{0})}^{- 4}$

Step 2.2.2

Simplify ${(1 + e^{0})}^{- 4}$ .

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Step 2.2.2.1

Anything raised to $0$ is $1$ .

$y = {(1 + 1)}^{- 4}$

Step 2.2.2.2

Add $1$ and $1$ .

$y = 2^{- 4}$

Step 2.2.2.3

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

$y = \frac{1}{2^{4}}$

Step 2.2.2.4

Raise $2$ to the power of $4$ .

$y = \frac{1}{16}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{16})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, \frac{1}{16})$

Step 4