Precalculus Examples

$y = - \log_{2} (- x)$

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 $x$ .

$0 = - \log_{2} (- x)$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $- \log_{2} (- x) = 0$ .

$- \log_{2} (- x) = 0$

Step 1.2.2

Divide each term in $- \log_{2} (- x) = 0$ by $- 1$ and simplify.

Tap for more steps...

Step 1.2.2.1

Divide each term in $- \log_{2} (- x) = 0$ by $- 1$ .

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

Step 1.2.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.2.2.2.2

Divide $\log_{2} (- x)$ by $1$ .

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

Step 1.2.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.2.3.1

Divide $0$ by $- 1$ .

$\log_{2} (- x) = 0$

Step 1.2.3

Rewrite $\log_{2} (- x) = 0$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$2^{0} = - x$

Step 1.2.4

Solve for $x$ .

Tap for more steps...

Step 1.2.4.1

Rewrite the equation as $- x = 2^{0}$ .

$- x = 2^{0}$

Step 1.2.4.2

Divide each term in $- x = 2^{0}$ by $- 1$ and simplify.

Tap for more steps...

Step 1.2.4.2.1

Divide each term in $- x = 2^{0}$ by $- 1$ .

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

Step 1.2.4.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.4.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.2.4.2.2.2

Divide $x$ by $1$ .

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

Step 1.2.4.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.4.2.3.1

Move the negative one from the denominator of $\frac{2^{0}}{- 1}$ .

$x = - 1 \cdot 2^{0}$

Step 1.2.4.2.3.2

Rewrite $- 1 \cdot 2^{0}$ as $- 2^{0}$ .

$x = - 2^{0}$

Step 1.2.4.2.3.3

Anything raised to $0$ is $1$ .

$x = - 1 \cdot 1$

Step 1.2.4.2.3.4

Multiply $- 1$ by $1$ .

$x = - 1$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 1, 0)$

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 $y$ .

$y = - \log_{2} (- (0))$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Remove parentheses.

$y = - \log_{2} (- (0))$

Step 2.2.2

Simplify the right side.

Tap for more steps...

Step 2.2.2.1

Multiply $- 1$ by $0$ .

$y = - \log_{2} (0)$

Step 2.2.2.2

The equation cannot be solved because it is undefined.

$Undefined$

Step 2.3

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

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(- 1, 0)$

y-intercept(s): $None$

Step 4