Algebra Examples

$f (x) = - 2 (\frac{1^{x}}{3})$

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 $x$ .

$0 = - 2 \frac{1^{x}}{3}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- 2 \frac{1^{x}}{3} = 0$ .

$- 2 \frac{1^{x}}{3} = 0$

Step 1.2.2

Simplify $- 2 \frac{1^{x}}{3}$ .

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Step 1.2.2.1

One to any power is one.

$- 2 (\frac{1}{3}) = 0$

Step 1.2.2.2

Combine $- 2$ and $\frac{1}{3}$ .

$\frac{- 2}{3} = 0$

Step 1.2.2.3

Move the negative in front of the fraction.

$- \frac{2}{3} = 0$

Step 1.2.3

Set the numerator equal to zero.

$2 = 0$

Step 1.2.4

Since $2 \neq 0$ , 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 $y$ .

$y = - 2 \frac{1^{0}}{3}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = - 2 \frac{1^{0}}{3}$

Step 2.2.2

Simplify $- 2 \frac{1^{0}}{3}$ .

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Step 2.2.2.1

Anything raised to $0$ is $1$ .

$y = - 2 (\frac{1}{3})$

Step 2.2.2.2

Combine $- 2$ and $\frac{1}{3}$ .

$y = \frac{- 2}{3}$

Step 2.2.2.3

Move the negative in front of the fraction.

$y = - \frac{2}{3}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{2}{3})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{2}{3})$

Step 4