Algebra Examples

$y = \frac{1}{2} {(6)}^{x + 1}$

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 $x$ .

$0 = \frac{1}{2} \cdot {(6)}^{x + 1}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{1}{2} \cdot 6^{x + 1} = 0$ .

$\frac{1}{2} \cdot 6^{x + 1} = 0$

Step 1.2.2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot 6^{x + 1}) = 2 \cdot 0$

Step 1.2.3

Simplify both sides of the equation.

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Step 1.2.3.1

Simplify the left side.

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Step 1.2.3.1.1

Simplify $2 (\frac{1}{2} \cdot 6^{x + 1})$ .

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Step 1.2.3.1.1.1

Combine $\frac{1}{2}$ and $6^{x + 1}$ .

$2 \frac{6^{x + 1}}{2} = 2 \cdot 0$

Step 1.2.3.1.1.2

Cancel the common factor of $2$ .

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Step 1.2.3.1.1.2.1

Cancel the common factor.

$2 \frac{6^{x + 1}}{2} = 2 \cdot 0$

Step 1.2.3.1.1.2.2

Rewrite the expression.

$6^{x + 1} = 2 \cdot 0$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply $2$ by $0$ .

$6^{x + 1} = 0$

Step 1.2.4

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

$\ln (6^{x + 1}) = \ln (0)$

Step 1.2.5

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

Undefined

Step 1.2.6

There is no solution for $6^{x + 1} = 0$

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 $y$ .

$y = \frac{1}{2} \cdot {(6)}^{(0) + 1}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{1}{2} \cdot 6^{0 + 1}$

Step 2.2.2

Remove parentheses.

$y = \frac{1}{2} \cdot {(6)}^{(0) + 1}$

Step 2.2.3

Simplify $\frac{1}{2} \cdot {(6)}^{(0) + 1}$ .

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Step 2.2.3.1

Add $0$ and $1$ .

$y = \frac{1}{2} \cdot 6^{1}$

Step 2.2.3.2

Evaluate the exponent.

$y = \frac{1}{2} \cdot 6$

Step 2.2.3.3

Cancel the common factor of $2$ .

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Step 2.2.3.3.1

Factor $2$ out of $6$ .

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

Step 2.2.3.3.2

Cancel the common factor.

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

Step 2.2.3.3.3

Rewrite the expression.

$y = 3$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 3)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 3)$

Step 4