Algebra Examples

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

Step 1

Find the x-intercepts.

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Step 1.1

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

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

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{1}{8} \cdot 4^{x + 1} = 0$ .

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

Step 1.2.2

Multiply both sides of the equation by $8$ .

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

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

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Step 1.2.3.1.1.1

Combine $\frac{1}{8}$ and $4^{x + 1}$ .

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

Step 1.2.3.1.1.2

Cancel the common factor of $8$ .

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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.

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

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply $8$ by $0$ .

$4^{x + 1} = 0$

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

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 $y$ .

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

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.

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

Step 2.3

y-intercept(s) in point form.

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