Algebra Examples

$f (x) = - 6 e^{x}$

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 $x$ .

$0 = - 6 e^{x}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- 6 e^{x} = 0$ .

$- 6 e^{x} = 0$

Step 1.2.2

Divide each term in $- 6 e^{x} = 0$ by $- 6$ and simplify.

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Step 1.2.2.1

Divide each term in $- 6 e^{x} = 0$ by $- 6$ .

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

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $- 6$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.2.1.2

Divide $e^{x}$ by $1$ .

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

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $0$ by $- 6$ .

$e^{x} = 0$

Step 1.2.3

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

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

Step 1.2.4

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

Undefined

Step 1.2.5

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

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 $y$ .

$y = - 6 e^{0}$

Step 2.2

Simplify $- 6 e^{0}$ .

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Step 2.2.1

Anything raised to $0$ is $1$ .

$y = - 6 \cdot 1$

Step 2.2.2

Multiply $- 6$ by $1$ .

$y = - 6$

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