Algebra Examples

f (x) = \frac{1}{8} \cdot 4^{x + 1}

$f (x) = \frac{1}{8} \cdot 4^{x + 1}$

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}{8} \cdot 4^{x + 1}

$0 = \frac{1}{8} \cdot 4^{x + 1}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as

\frac{1}{8} \cdot 4^{x + 1} = 0

$\frac{1}{8} \cdot 4^{x + 1} = 0$ .

\frac{1}{8} \cdot 4^{x + 1} = 0

$\frac{1}{8} \cdot 4^{x + 1} = 0$

Step 1.2.2

Multiply both sides of the equation by

8

$8$ .

8 (\frac{1}{8} \cdot 4^{x + 1}) = 8 \cdot 0

$8 (\frac{1}{8} \cdot 4^{x + 1}) = 8 \cdot 0$

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

8 (\frac{1}{8} \cdot 4^{x + 1})

$8 (\frac{1}{8} \cdot 4^{x + 1})$ .

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Step 1.2.3.1.1.1

Combine

\frac{1}{8}

$\frac{1}{8}$ and

4^{x + 1}

$4^{x + 1}$ .

8 \frac{4^{x + 1}}{8} = 8 \cdot 0

$8 \frac{4^{x + 1}}{8} = 8 \cdot 0$

Step 1.2.3.1.1.2

Cancel the common factor of

8

$8$ .

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Step 1.2.3.1.1.2.1

Cancel the common factor.

$8 \frac{4^{x + 1}}{8} = 8 \cdot 0$

Step 1.2.3.1.1.2.2

Rewrite the expression.

$4^{x + 1} = 8 \cdot 0$

$4^{x + 1} = 8 \cdot 0$

$4^{x + 1} = 8 \cdot 0$

$4^{x + 1} = 8 \cdot 0$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply

$8$ by

$0$ .

$4^{x + 1} = 0$

$4^{x + 1} = 0$

$4^{x + 1} = 0$

Step 1.2.4

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

$\ln (4^{x + 1}) = \ln (0)$

Step 1.2.5

The equation cannot be solved because

$\ln (0)$ is undefined.

Undefined

Step 1.2.6

There is no solution for

$4^{x + 1} = 0$

No solution

No solution

Step 1.3

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

$0$ for

$y$ and solve for

$x$ .

x-intercept(s):

$None$

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

$y$ .

$y = \frac{1}{8} \cdot 4^{(0) + 1}$

Step 2.2

Simplify

$\frac{1}{8} \cdot 4^{(0) + 1}$ .

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Step 2.2.1

Add

$0$ and

$1$ .

$y = \frac{1}{8} \cdot 4^{1}$

Step 2.2.2

Evaluate the exponent.

$y = \frac{1}{8} \cdot 4$

Step 2.2.3

Cancel the common factor of

$4$ .

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Step 2.2.3.1

Factor

$4$ out of

$8$ .

$y = \frac{1}{4 (2)} \cdot 4$

Step 2.2.3.2

Cancel the common factor.

$y = \frac{1}{4 \cdot 2} \cdot 4$

Step 2.2.3.3

Rewrite the expression.

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

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

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

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

$(0, \frac{1}{2})$

y-intercept(s):

$(0, \frac{1}{2})$

Step 3

List the intersections.

x-intercept(s):

$None$

y-intercept(s):

$(0, \frac{1}{2})$

Step 4

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