Algebra Examples

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

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

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

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

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

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

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

\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

$2$ .

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

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

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})

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

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Step 1.2.3.1.1.1

Combine

\frac{1}{2}

$\frac{1}{2}$ and

6^{x + 1}

$6^{x + 1}$ .

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

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

Step 1.2.3.1.1.2

Cancel the common factor of

2

$2$ .

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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

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

Step 1.2.3.1.1.2.2

Rewrite the expression.

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

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

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

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

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

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

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

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

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply

2

$2$ by

0

$0$ .

6^{x + 1} = 0

$6^{x + 1} = 0$

6^{x + 1} = 0

$6^{x + 1} = 0$

6^{x + 1} = 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)

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

Step 1.2.5

The equation cannot be solved because

\ln (0)

$\ln (0)$ is undefined.

Undefined

Step 1.2.6

There is no solution for

6^{x + 1} = 0

$6^{x + 1} = 0$

No solution

No solution

Step 1.3

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

x-intercept(s):

None

$None$

x-intercept(s):

None

$None$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in

0

$0$ for

x

$x$ and solve for

y

$y$ .

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

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

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

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

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

Step 2.2.2

Remove parentheses.

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

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

Step 2.2.3

Simplify

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

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

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Step 2.2.3.1

Add

0

$0$ and

1

$1$ .

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

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

Step 2.2.3.2

Evaluate the exponent.

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

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

Step 2.2.3.3

Cancel the common factor of

2

$2$ .

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Step 2.2.3.3.1

Factor

2

$2$ out of

6

$6$ .

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

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

Step 2.2.3.3.2

Cancel the common factor.

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

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

Step 2.2.3.3.3

Rewrite the expression.

y = 3

$y = 3$

y = 3

$y = 3$

y = 3

$y = 3$

y = 3

$y = 3$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

(0, 3)

$(0, 3)$

y-intercept(s):

(0, 3)

$(0, 3)$

Step 3

List the intersections.

x-intercept(s):

None

$None$

y-intercept(s):

(0, 3)

$(0, 3)$

Step 4

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$